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Content and Activities for
Term 1, 2& 3
Physics S6
Experimental Version
Kigali, August, 2018
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Copyright
© 2018 Rwanda Education Board
All rights reserved.
This document is the property of Rwanda Education Board.
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DETAILED CONTENTS
DETAILED CONTENTS ....................................................................................................... iii
UNIT1: SOUND WAVES ....................................................................................................... 1
1.1 CHARACTERISTICS AND PROPERTIES OF SOUND WAVES .............................................................. 2 1.1.1 Properties of sound waves ............................................................................................................................ 3 1.1.2 Characteristics of sound waves...................................................................................................................... 3 1.1.3 Checking my progress .................................................................................................................................... 7
1.2 PRODUCTION OF STATIONARY SOUND WAVES ........................................................................... 9 1.2.1 Sound in pipes ................................................................................................................................................ 9 1.2.2 Vibrating strings ........................................................................................................................................... 14 1.2.3. Wave Interference and Superposition ........................................................................................................ 17 1.2.4 Checking my progress .................................................................................................................................. 22
1.3 CHARACTERISTICS OF MUSICAL NOTES ..................................................................................... 24 1.3.1. Pitch and frequency .................................................................................................................................... 24 1.3.2 Intensity and amplitude ............................................................................................................................... 24 1.3.3 Quality or timbre ......................................................................................................................................... 26 1.3.4 Checking my progress .................................................................................................................................. 27
1.4 APPLICATIONS OF SOUND WAVES ............................................................................................ 28 1.4.1 The Doppler Effect ....................................................................................................................................... 28 1.4.2 Uses of Ultrasonic ........................................................................................................................................ 31 1.4.3 Uses of infrasonic ......................................................................................................................................... 33 1.4.4 Checking my progress .................................................................................................................................. 34
1.5 END UNIT ASSESSMENT ............................................................................................................ 35 1.5.1 Multiple choices question ............................................................................................................................ 35 1.5.2 Structured questions ................................................................................................................................... 36 1.5.3 Essay type question ..................................................................................................................................... 37
UNIT 2: CLIMATE CHANGE AND GREENHOUSE EFFECT ............................................ 38
2.1 SCIENTIFIC PROCESS BEHIND CLIMATE CHANGE ........................................................................ 39 2.1.1 Black body radiation .................................................................................................................................... 39 2.1.2 Laws of black body radiation ....................................................................................................................... 39 2.1.3 Black body radiation curves ......................................................................................................................... 41 2.1.4 Checking my progress .................................................................................................................................. 42
2.2 INTENSITY OF THE SUN’S RADIATION REACHING PLANETS ......................................................... 43 2.2.1 Intensity of the sun’s radiation and albedo ................................................................................................. 43 2.2.2 Factors affecting Earth’s albedo .................................................................................................................. 46 2.2.3 Checking my progress .................................................................................................................................. 47
2.3 GREENHOUSE EFFECTS ............................................................................................................. 48 2.3.1 Greenhouse gases ........................................................................................................................................ 49 2.3.2 Impact of greenhouse effect on climate change. ........................................................................................ 51 2.3.3 Global warming ............................................................................................................................................ 51 2.3.4 Checking my progress .................................................................................................................................. 52
2.4 CLIMATE CHANGE .................................................................................................................... 53 2.4.1 Climate change and related facts ................................................................................................................ 54 2.4.2 Causes of climate change. ........................................................................................................................... 55 2.4.3 Checking my progress .................................................................................................................................. 57
2.5 CLIMATE CHANGE MITIGATION ................................................................................................ 60 2.5.1 Climate change mitigation ........................................................................................................................... 60 2.5.2 Mitigation and adaptation ........................................................................................................................... 61 2.5.3 Checking my progress .................................................................................................................................. 63
2.6 END UNIT ASSESSMENT ............................................................................................................ 64 2.6.1 Multiple choice type questions. ................................................................................................................... 64
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2.6.2 Structured questions ................................................................................................................................... 65 2.6.3 Essay type questions .................................................................................................................................... 66
UNIT 3: APPLICATION OF PHYSICS IN AGRICULTURE ................................................ 67
3.1 ATMOSPHERE AND ITS CONSTITUENTS ..................................................................................... 68 3.1.1 Atmosphere ................................................................................................................................................. 68 3.1.2 Composition of the Atmosphere ................................................................................................................. 68 3.1.3 Layers of the atmosphere. ........................................................................................................................... 69 3.1.4 Checking my progress .................................................................................................................................. 73
3.2 HEAT AND MASS TRANSFER ..................................................................................................... 75 3.2.1 Modes of Heat Transfer ............................................................................................................................... 75 3.2.2 Environmental heat energy and mass transfer ............................................................................................ 77 3.2.3 Water vapour in the atmosphere. ............................................................................................................... 77 3.2.4 Variation in Atmospheric Pressure .............................................................................................................. 78 3.2.5 Air density and water vapour with altitude ................................................................................................. 78 3.2.6 Checking my progress .................................................................................................................................. 79
3.3 PHYSICAL PROPERTIES OF SOIL ................................................................................................. 80 3.3.1 Soil texture ................................................................................................................................................... 82 3.3.2 Soil structure ................................................................................................................................................ 83 3.3.3 Checking my progress: ................................................................................................................................. 84
3.4 MECHANICAL WEATHERING ..................................................................................................... 85 3.4.1 Concepts of mechanical weathering ............................................................................................................ 85 3.4.2 Causes of mechanical weathering ............................................................................................................... 86 3.4.3 Factors influencing the type and rate of rock weathering ........................................................................... 90 3.4.4 Checking my progress .................................................................................................................................. 92
3.5 END UNIT ASSESSMENT ............................................................................................................ 94 3.5.1 Multiple choices questions .......................................................................................................................... 94 3.5.2 Structured Questions ................................................................................................................................... 95 3.5.3 Essay type questions .................................................................................................................................... 96
UNIT 4: EARTHQUAKES, LANDSLIDES, TSUNAMI, FLOODS AND CYCLONES. .......... 97
4.1 The earthquake ........................................................................................................................ 98 4.1.1 Origin of earthquakes .................................................................................................................................. 99 4.1.2 Intensity of earthquakes .............................................................................................................................. 99 4.1.3 Measurement of the size of earthquakes .................................................................................................. 100 4.1.4 Types of earthquake waves ....................................................................................................................... 100 4.1.5 Causes of earthquake ................................................................................................................................ 101 4.1.6 Effects of earthquakes ............................................................................................................................... 102 4.1.7 Safety measures on earthquakes ............................................................................................................... 103 4.1.8 Checking my progress ................................................................................................................................ 104
4.2. LANDSLIDES. ......................................................................................................................... 105 4.2.1 Definition of landslide ................................................................................................................................ 105 4.2.2 Causes of landslide .................................................................................................................................... 106 4.2.3. Effect of landslides .................................................................................................................................... 106 4.2.4 Safety measures of landslides .................................................................................................................... 107 4.2.5 Checking my progress ................................................................................................................................ 108
4.3. TSUNAMI .............................................................................................................................. 109 4.3.1 Definition of Tsunami. ............................................................................................................................... 109 4.3.2 Causes of Tsunami ..................................................................................................................................... 111 4.3.3 Effects of Tsunami...................................................................................................................................... 111 4.3.4 Prevention of tsunami ............................................................................................................................... 112 4.3.5 Checking my progress. ............................................................................................................................... 112
4.4. FLOODS................................................................................................................................. 113 4.4.1 concept of flood ......................................................................................................................................... 113 4.4.2 Types of floods ........................................................................................................................................... 114
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4.4.3 Causes of floods ......................................................................................................................................... 114 4.4.4 Consequences of floods ............................................................................................................................. 115 4.4.5 Floods and safety measures ...................................................................................................................... 115 4.4.6 Checking my progress. ............................................................................................................................... 116
4.5. CYCLONES AND ANTICYCLONES ............................................................................................. 117 4.5.1 Types of cyclones ....................................................................................................................................... 118 4.5.2 Effect of Cyclone ........................................................................................................................................ 119 4.5.3 Safety and emergency measures of cyclones. ........................................................................................... 120 4.5.4 Anticyclone ................................................................................................................................................ 121 4.5.5 Types of anticyclones ................................................................................................................................. 121 4.5.6 Checking my progress ................................................................................................................................ 122
4.6 END UNIT ASSESSMENT .......................................................................................................... 123 4.6.1 Multiple choices. ........................................................................................................................................ 123 4.6.2 Structured Questions ................................................................................................................................. 123 4.6.3 Essay type questions .................................................................................................................................. 123
UNIT 5. ATOMIC NUCLEI AND RADIOACTIVE DECAY ................................................ 124
5.1 ATOMIC NUCLEI-NUCLIDE ....................................................................................................... 126 5.1.1 Standard representation of the atomic nucleus ........................................................................................ 126 5.1.2 Classification .............................................................................................................................................. 126 5.1.3 Units and dimensions in nuclear physics ................................................................................................... 127 5.1.4 Working principle a mass spectrometer .................................................................................................... 129 5.1.5 Checking my progress ................................................................................................................................ 130
5.2 MASS DEFECT AND BIDING ENERGY ........................................................................................ 131 5.2.1 Mass defect ................................................................................................................................................ 131 5.2.2 Einstein mass-energy relation.................................................................................................................... 132 5.2.3 Binding energy ........................................................................................................................................... 133 5.2.4 Binding energy per nucleon and stability .................................................................................................. 133 5.2.5 Checking my progress ................................................................................................................................ 135
5.3 RADIOACTIVITY AND NUCLEAR STABILITY ............................................................................... 136 5.3.1 Radioactive decay of a single parent ......................................................................................................... 137 5.3.2 Characteristics of radioactive substances .................................................................................................. 138 5.3.3 Nuclear fission and Fusion ......................................................................................................................... 142 5.3.4 Radiation detectors ................................................................................................................................... 143 5.3.5 Checking my progress ................................................................................................................................ 145
5.4 APPLICATION OF RADIOACTIVITY ........................................................................................... 147 5.4.1 Industry ...................................................................................................................................................... 147 5.4.2 Tracer studies............................................................................................................................................. 148 5.4.3 Nuclear power stations .............................................................................................................................. 148 5.4.4 Nuclear fusion ............................................................................................................................................ 148 5.4.5 Medicine .................................................................................................................................................... 149 5.4.6 Food preservation ...................................................................................................................................... 150 5.4.7 Radiocarbon dating .................................................................................................................................... 150 5.4.8 Agricultural uses ........................................................................................................................................ 151 5.4.9 Checking my progress ................................................................................................................................ 151
5.5 HAZARDS AND SAFETY PRECAUTIONS OF WHEN HANDLING RADIATIONS ................................ 152 5.5.1 Dangers of radioactivity ............................................................................................................................. 152 5.5.2 Safety precautions when Handling Radiations .......................................................................................... 152
5.6 END UNIT ASSESSMENT .......................................................................................................... 155 5.6.1 Multiple choice questions .......................................................................................................................... 155 5.6.2 Structured questions ................................................................................................................................. 157 5.6.3 Question of research ................................................................................................................................. 159
UNIT 6: APPLICATIONS OF OPTICAL FIBER IN TELECOMMUNICATION SYSTEMS.
............................................................................................................................................ 160
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6.1 PRINCIPLES OF OPERATIONS OF OPTICAL FIBERS ..................................................................... 161 6.1.1 Definition ................................................................................................................................................... 161 6.1.2 Refractive index of light ............................................................................................................................. 163 6.1.3 Total internal reflection ............................................................................................................................. 163 6.1.4 Checking my progress ................................................................................................................................ 167
6.2 TYPES OF OPTICAL FIBERS ....................................................................................................... 169 6.2.1 Monomode fibers ...................................................................................................................................... 169 6.2.2 Multimode fibers ....................................................................................................................................... 169 6.2.3 Special-purpose optical fiber ..................................................................................................................... 170 6.2.4 Checking my progress ................................................................................................................................ 171
6.3 MECHANISM OF ATTENUATION .............................................................................................. 172 6.3.1 Light scattering and absorption ................................................................................................................. 173 6.3.2 Measures to avoid Attenuation ................................................................................................................. 174 6.3.3 Checking my progress ................................................................................................................................ 174
6.4 OPTICAL TRANSMITTER AND OPTICAL RECEIVER ..................................................................... 175 6.4.1 Transmitters ............................................................................................................................................... 175 6.4.2 The Optical Receivers................................................................................................................................. 176 6.4.3 Checking my progress ................................................................................................................................ 176
6.5. USES OF OPTICAL FIBERS ....................................................................................................... 177 6.5.1 Telecommunications Industry ................................................................................................................... 177 6.5.2 Medicine Industry ...................................................................................................................................... 177 6.5.3 Checking my progress ................................................................................................................................ 177
6.6 ADVANTAGES AND DISADVANTAGES OF OPTICAL FIBERS ........................................................ 178 6.6.1 Advantages ................................................................................................................................................ 178 6.6.2 Disadvantages ............................................................................................................................................ 178 6.6.3 Checking my progress ................................................................................................................................ 178
6.7. END UNIT ASSESSMENT ......................................................................................................... 179
UNIT 7: BLOCK DIAGRAM OF TELECOMMUNICATION .............................................. 181
7.1 OPERATING PRINCIPLE OF MICROPHONE ................................................................................ 183
7.2 CHANNELS OF SIGNAL TRANSMISSION .................................................................................... 184 7.2.1 Amplitude modulation (AM) ...................................................................................................................... 184 7.2.2 Frequency modulation (FM). ..................................................................................................................... 185 7.2.3 Short wave (SW) ........................................................................................................................................ 186 7.2.4 Medium wave (MW) .................................................................................................................................. 186 7.2.5 Checking my progress ................................................................................................................................ 187
7.3 CARRIER WAVE AND MODULATOR ......................................................................................... 188 7.3.1 Concept of carrier wave modulation ......................................................................................................... 188 7.3.2 Checking my progress ................................................................................................................................ 188
7.4 OSCIALLATOR, RADIO FREQUENCY AMPLIFIER AND POWER AMPLIFIER ................................... 190 7.4.1 Oscillator .................................................................................................................................................... 190 7.4.2 Radio frequency amplifier ......................................................................................................................... 191 7.4.3 Power Amplifier ......................................................................................................................................... 192 7.4.4 Checking my progress ................................................................................................................................ 193
7.5 ANTENNAS ............................................................................................................................. 194 7.5.1 Types of antennas ...................................................................................................................................... 194 7.5.2 Checking my progress ................................................................................................................................ 196
7.6 BLOCK DIAGRAMS OF TELECOMMUNICATION ......................................................................... 197 7.6.1 Simple radio transmitter ............................................................................................................................ 199 7.6.2 Simple radio receiver ................................................................................................................................. 200 7.6.3 Wireless Radio Communication ................................................................................................................. 201 7.6.4 Checking my progress ................................................................................................................................ 202
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7.7 END UNIT ASSESSMENT .......................................................................................................... 202 7.7.1 Multiple choices ......................................................................................................................................... 202 7.7.2 Structured questions ................................................................................................................................. 202 7.7.3 Essay question ........................................................................................................................................... 203
UNIT 8: NATURE OF PARTICLES AND THEIR INTERACTIONS .................................. 204
8.1 ELEMENTARY PARTICLES. ....................................................................................................... 205 8.1.1 Introduction ............................................................................................................................................... 205 8.1.2 Checking my progress ................................................................................................................................ 206
8.2 CLASSIFICATION OF ELEMENTARY PARTICLES. ......................................................................... 208 8.2.1 Classification of particles by mass ............................................................................................................. 208 8.2.2 Classification of particles by spin. .............................................................................................................. 209 8.2.3 Checking my progress ................................................................................................................................ 210
8.3 ANTI PARTICLE AND PAULI’S EXCLUSION PRINCIPLE ................................................................ 212 8.3.1 Concept of particle and antiparticle .......................................................................................................... 212 8.3.2 Pauli’s exclusion principle, ......................................................................................................................... 212 8.3.3 Checking my progress ................................................................................................................................ 213
8.4 FUNDAMENTAL INTERACTIONS BY PARTICLE EXCHANGE ......................................................... 214 8.4.1 Forces and Interactions ............................................................................................................................. 214 8.4.2 Checking my progress ................................................................................................................................ 216
8.5 UNCERTAINTY PRINCIPLE AND PARTICLE CREATION ................................................................ 217 8.5.1 The concept of uncertainty principle ......................................................................................................... 217 8.5.2 Checking my progress ................................................................................................................................ 219
8.6 MATTER AND ANTIMATTER (PAIR PRODUCTION AND ANNIHILATION) .................................... 220 8.6. 1 Introduction .............................................................................................................................................. 220 8.6.2 Pair production and annihilation ............................................................................................................... 220 8.6.3 Application of antimatter .......................................................................................................................... 221 8.6.4 Checking my progress ................................................................................................................................ 222
8.7 END UNIT ASSESSMENT .......................................................................................................... 223 8.7.1 Multiple choices ......................................................................................................................................... 223 8.7.2 Structured questions ................................................................................................................................. 223 8.7.3 Essay question ........................................................................................................................................... 224
UNIT 9: PROPERTIES AND BASIC PRINCIPLES OF QUARKS. ..................................... 225
9.1 INTRODUCTION ...................................................................................................................... 225 9.1.2 Checking my progress ................................................................................................................................ 227
9.2 TYPES OF QUARKS .................................................................................................................. 229
9.3 BARYON NUMBER, LEPTON NUMBER AND THEIR LAWS OF CONSERVATION ............................ 231
9.5 SPIN STRUCTURES OF HADRONS (HADRONS AND MESONS) .................................................... 234
9.6 COLOR IN FORMING OF BOUND STATES OF QUARKS. .............................................................. 238 9.6.1 Bound state of quarks ................................................................................................................................ 238 9.6.2 Color in forming of bound states of quarks. .............................................................................................. 239 9.6.3 Colour as component of quarks and gluons .............................................................................................. 239 9.6.4 Checking my understanding ...................................................................................................................... 241
9.7 END UNIT ASSEMENT ............................................................................................................. 241 9.7.1 Multiple choices ......................................................................................................................................... 241 9.7.2 Structured questions ................................................................................................................................. 242
UNIT10: EFFECT OF X-RAYS .......................................................................................... 245
10.1 PRODUCTION OF X-RAYS AND THEIR PROPERTIES ................................................................. 246 10.1.1 X-ray production ...................................................................................................................................... 246 10.1.2 Types of X-rays ......................................................................................................................................... 247
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10.1.3 Properties of X-rays ................................................................................................................................. 247 10.1.4 Checking my progress .............................................................................................................................. 248
10.2 THE ORIGINS AND CHARACTERISTIC FEATURES OF AN X-RAY SPECTRUM ............................... 249 10.2.1 Variation of the X-ray intensity with wavelength .................................................................................... 249 10.2.2 Origin of the continuous spectrum .......................................................................................................... 250 10.2.3 Origin of characteristic lines .................................................................................................................... 251 10.2.4 Checking my progress .............................................................................................................................. 252
10.3 APPLICATIONS AND DANGERS OF X-RAYS ............................................................................. 253 10.3.1 In medicine .............................................................................................................................................. 253 10.3.2 Examining luggage cargo and security. .................................................................................................... 255 10.3.3 In industry ................................................................................................................................................ 255 10.3.4 In scientific research ................................................................................................................................ 256 10.3.5 Dangers of X-rays ..................................................................................................................................... 256 10.3.6 Safety precaution measures of dangers caused by X-rays....................................................................... 256 10.3.7 Checking my progress .............................................................................................................................. 257
10.4 PROBLEMS INVOLVING ACCELERATING POTENTIAL AND MINIMUM WAVELENGTH. .............. 258 10.4.1 Accelerating potential and minimum wavelength ................................................................................... 258 10.4.2 Checking my progress .............................................................................................................................. 261
10.5 END UNIT ASSESSMENT ........................................................................................................ 262 10.5.1 Multiple choices ....................................................................................................................................... 262 10.5.2 Structured questions ............................................................................................................................... 262
UNIT 11: EFFECTS OF LASER. ....................................................................................... 265
11.1 Concept of LASER ................................................................................................................. 266 11.1.1 Absorption, Spontaneous emission and Stimulated emission................................................................. 266 11.1.2 Laser principle .......................................................................................................................................... 269 11.1.3 Population inversion ................................................................................................................................ 271 11.1.4 Laser structure ......................................................................................................................................... 272 11.1.5 Checking my progress .............................................................................................................................. 273
11.2 PROPERTIES OF LASER LIGHT ................................................................................................ 275 11.2.1 Coherence ................................................................................................................................................ 275 11.2.2 Monochromaticity ................................................................................................................................... 275 11.2.3 Collimation or Directionality .................................................................................................................... 275 11.2.4 Checking my progress .............................................................................................................................. 276
11.3 APPLICATIONS AND DANGERS OF MISUSE OF LASER ............................................................. 277 11.3.1 Applications of lasers. .............................................................................................................................. 277 11.3.2 Dangers of lasers ...................................................................................................................................... 280 11.3.3 Precaution measures to avoid negative effects of lasers ........................................................................ 280 11.3.4 Checking my progress .............................................................................................................................. 281
11.4 END UNIT ASSESSMENT ........................................................................................................ 282 11.4.1 Multiple choice ........................................................................................................................................ 282 11.4.2 Structured questions ............................................................................................................................... 284
UNIT 12: MEDICAL IMAGING ......................................................................................... 285
12.1 X-RAY IMAGING. .................................................................................................................. 287 12.1.1 Interaction of X-rays with matter. ........................................................................................................... 287 12.1.2 X-rays Imaging Techniques ...................................................................................................................... 290 12.1.3 Checking my progress .............................................................................................................................. 296
12.2 ULTRASONIC IMAGING ......................................................................................................... 297 12.2.1 Basics of Ultra sound and its production ................................................................................................. 297 12.2.2 Interaction of sound waves with different structure inside the body ..................................................... 297 12.2.3 Ultrasonic imaging techniques................................................................................................................. 299 12.2.4 Checking my progress .............................................................................................................................. 303
12.3 SCINTIGRAPHY (NUCLEAR MEDICINE) ................................................................................... 303
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12.3.1 Physics of scintigraphy and terminology ................................................................................................. 303 12.3.2 Basic functioning of radionuclide scan .................................................................................................... 304 12.3.3 Limitations and disadvantages of scintigraphy ........................................................................................ 305 12.3.4 Checking my progress .............................................................................................................................. 305
12.4 MAGNETIC RESONANCE IMAGING (MRI) ............................................................................... 306 12.4.1. MRI physics and terminology. ................................................................................................................. 306 12.4.2. The magnetism of the body .................................................................................................................... 308 12.4.3. Magnetic Resonance Imaging (MRI). ..................................................................................................... 308 12.4.4. Functional of MRI Scan ........................................................................................................................... 309 12.4.5 Advantage and disadvantages of MRI. .................................................................................................... 310 12.4.7. Checking my progress ............................................................................................................................. 311
12.5 ENDOSCOPY ......................................................................................................................... 311 12.3.1 Description ............................................................................................................................................... 311 12.3.2 Upper endoscopy ..................................................................................................................................... 311 12.3.3. How is the upper endoscopy performed? .............................................................................................. 312 12.3.4. Advantages and disadvantages of endoscopy ........................................................................................ 313 12.3.5 Checking my progress .............................................................................................................................. 314 12.3.6. HAZARDS ASSOCIATED WITH MEDICAL IMAGING .................................................................................. 314
END UNIT ASSESSMENT ............................................................................................................... 316
Part II: Structured questions ........................................................................................................ 317
UNIT 13: RADIATIONS AND MEDICINE ........................................................................ 319
13.1 RADIATION DOSE ................................................................................................................. 320 13.1.1 Ionization and non-ionization radiations ................................................................................................. 320 13.1.2 Radiation penetration in body tissue ....................................................................................................... 322 13.1.3 Radiation dosimetry ................................................................................................................................. 324 13.1.4 Radiation exposure .................................................................................................................................. 325 13.1.5 Absorbed radiation dose.......................................................................................................................... 325 13.1.6 Quality factors.......................................................................................................................................... 326 13.1.7 Equivalent dose........................................................................................................................................ 327 13.1.8 Radiation protection ................................................................................................................................ 327 13.1.9 Checking my progress .............................................................................................................................. 328
13.2 BIOLOGICAL EFFECTS OF RADIATION EXPOSURE .................................................................... 329 13.2.1 Deterministic and stochastic effects: ....................................................................................................... 329 13.2.2 Effects of radiation exposure ................................................................................................................... 331 13.2.3 Safety precautions for handling radiations .............................................................................................. 333 13.2.3 Checking my progress .............................................................................................................................. 335
13.3 CONCEPT OF BALANCED RISK. ............................................................................................... 336 13.3.1 Risks of ionizing radiation in medical treatment ..................................................................................... 336 13.3.2 Human Error and Unintended Events ...................................................................................................... 336 13.3.3 Comparison of risks in the use of ionizing radiation ................................................................................ 336 13.3.4 Checking my progress .............................................................................................................................. 337
13.4 THE HALF-LIVES: PHYSICAL, BIOLOGICAL, AND EFFECTIVE ...................................................... 338 13.4.1 Physical half Lives .................................................................................................................................... 338 14.4.2 Biological half lives ................................................................................................................................... 338 13.4.3 Effective half lives .................................................................................................................................... 339 13.4.4 Checking my progress .............................................................................................................................. 340
13.5 END UNIT ASSESSMENT ......................................................................................... 341 13.5.1 Multiple choice ........................................................................................................................................ 341 13.5.2 Structured questions ............................................................................................................................... 341 13.5.3 Essay questions ........................................................................................................................................ 342
UNIT 14: COSMOLOGY, GALAXIES AND EXPANSION OF UNIVERSE ........................ 343
14.1 GALAXIES AND CLUSTERS ..................................................................................................... 344
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14.1.1 The structure of the Milky Way Galaxy ................................................................................................... 344 14.1.2 Types of galaxies ...................................................................................................................................... 346 14.1.3 Clusters of galaxies .................................................................................................................................. 349 14.1.4 Checking my progress .............................................................................................................................. 351
14.2 COSMOLOGY ........................................................................................................................ 352 14.2.1 Doppler shift due to cosmic expansion.................................................................................................... 352 14.2.2 The Hubble’s law ...................................................................................................................................... 355 14.2.4 The Big Bang theory and expansion of Universe ..................................................................................... 357 14.2.4 Stellar evolution ....................................................................................................................................... 360 14.2.5 Checking my progress .............................................................................................................................. 364
14.3 END UNIT ASSESSMENT ........................................................................................................ 366 14.3.1 Multiple choices: ...................................................................................................................................... 366 14.3.2 Solve these problems ............................................................................................................................... 366
Bibliography ........................................................................................................................ 370
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UNIT1: SOUND WAVES
Fig.1. 1: People listening to music
Key unit Competence
By the end of the unit I should be able to analyze the effects of sound waves in elastic medium
My goals
Describe how sound propagates through a substance
Give the characteristics of sound.
Relate loudness and pitch to amplitude and frequency
Carry out calculations relating decibels and intensity
Establish relationship between characteristics of notes and sound waves
Explain beats and establish beat frequency
Explain Doppler – Fizeau effect.
Give examples of musical pipe instruments.
Establish the fundamental frequency and 2nd harmonic, 3rd harmonic, in vibrating strings and in
pipes
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Introductory activity: What properties explain most the behavior of sound?
1. Most people like to listen to music, but hardly anyone likes to listen to noise. What is the
difference between a musical sound and noise?
2. A guitarist plays any note. The sound is made by the vibration of the guitar string and propagates
as a wave through the air and reaches your ear. Which of the following statement is the right?
(a) The vibration on the string and the vibration in the air have the same wavelength.
(b) They have the same frequency.
(c) They have the same speed.
(d) None of the above is the same in the air as it is on the string.
1.1 CHARACTERISTICS AND PROPERTIES OF SOUND WAVES
Activity 1.1: Properties of sound
Read the scenario below and answer the questions that follow.
On an interview for Physics placement in a certain school in Rwanda, Claudette a S.6 leaver who had
applied for the job was asked about sound waves during the interview.
She was asked to state the properties of sound waves. Confidently, she responded that the properties
are reflection, refraction, diffraction and interference. This was enough to make Claudette pass
the first level of the interview.
However, in the second step, she was required to discuss different media in which sound waves can
propagate. Claudette started discussing these different media. What surprised the interviewer was
Claudette’s ability to relate sound waves to other kinds of waves stating that these waves behaves the
same way when they pass from one medium to another.
Looking at Claudette’s face, the interviewer asked her to discuss the laws governing reflection and
refraction of sound waves. With a smile, she started by saying that since sound waves have the
same properties as for light; these laws therefore do not change.
As she was attempting to state them, the interviewer stopped her and congratulated her upon her
confidence and bravery she showed in the room. She was directly told that she was successful and
she was given the job. Claudette is now working as assistant S2 Physics teacher and doubles as a
Physics laboratory attendant.
Questions
a. Explain the meaning of underlined terms used in the text above?
b. Do you think, it was 100% correct for Claudette to relate sound waves to light waves? Explain?
c. There is somewhere where she was asked to discuss the different media in which sound waves can
propagate. Discuss these different media and talk about speed of sound waves in the stated media.
d. In one of the paragraph, Claudette said that the laws governing reflection and refraction of sound
waves were similar to those of light. Can you explain these laws (Use diagrams where possible)
e. Assuming that you were an interviewer and the interview was out of 80.What mark would you
award to Claudette? Why?
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1.1.1 Properties of sound waves
Most of us start our lives by producing sound waves! We spend much of our life surrounded by
objects which produce sound waves. Most machines in use vibrate and produce sound so the only
sure way to silence them would be to put them in vacuum where there would be no surrounding
medium for the vibrating surfaces of the machine to push against, hence no sound waves. Some
physiologists are concerned with how speech is produced, how speech impairment might be
corrected, how hearing loss can be alleviated.
Sound is associated with our sense of hearing and, therefore, with the physiology of our ears that
intercept the sound and the psychology of our brain which interprets the sensations that reach our
ears. Sound waves are longitudinal mechanical waves that can travel through solids, liquids, or gases.
As the sound wave propagates, many interactions can occur, including reflection, refraction,
diffraction and interference. When a sound wave hits a surface, a part of the energy gets scattered
while a part of it is absorbed. Absorption is the phenomenon of the wave where the energy of sound
wave gets transformed from one form to another. The high frequency sound waves are more easily
absorbed than low frequency sounds. It happens most with the soft materials.
1.1.2 Characteristics of sound waves
Activity 1.2 Characteristics of sound waves
1. How to calculate the speed of sound waves in different materials.
2. How to calculate the intensity of a sound wave.
3. From the Fig.1.2, can you hear the ultrasound waves that a bat uses for echolocation? Why or
why not?
Fig.1. 2: Range of frequencies heard by various animals and human (Randall & Knight., Physics for scientists and
engineers: Stategic approach., 2008)
Usually, the characteristics used to describe waves are period, frequency, wavelength, and amplitude.
a) Frequency ranges
Any periodic motion has a frequency, which is the number of complete cycles in a second and a
period which is the time used to complete one cycle. While the frequency is measured in Hertz (Hz),
the period is measured in seconds (s).
4
For a wave, the frequency is the number of wave cycles that pass a point in a second. A wave’s
frequency equals the frequency of the vibrating source producing the wave.
Sound waves are classified into three categories that cover different frequency ranges:
- Audible sound lies within the range of sensitivity of the human ear. They can be generated in a
variety of ways, such as musical instruments, human voices, or loudspeakers. It is almost
impossible to hear sounds outside the range of 20 Hz to 20 kHz. These are the limits of audibility
for human beings but the range decreases with age.
- Infrasonic waves have frequencies below the audible range. They are sound waves with
frequencies that are below 20 Hz limit. Some animals such as elephants can use infrasonic waves
to communicate with each other, even when they are separated by many kilometers. Rhinoceros
also use infrasonic as low as 5 Hz to call one another.
- Ultrasonic waves have frequencies above the audible range. They are sound waves whose
frequencies are higher than 20 KHz. You may have used a “silent” whistle to retrieve your dog.
The ultrasonic sound emitted by that device is easily heard by dogs, although humans cannot
detect it at all. Ultrasonic waves are also used in medical imaging.
Many animals hear a much wider range of frequencies than human beings do. For example, dog
whistles vibrate at a higher frequency than the human ear can detect, while evidence suggests that
dolphins and whales communicate at frequencies beyond human hearing (ultrasound) (Cutnell &
Johnson, 2006).
b) Wavelength
Wavelength is the distance covered by a wave in a period. It is represented by the separation
between a point on one wave and a similar point on the next cycle of the wave. For a transverse
wave, wavelength is measured between adjacent crests or between adjacent troughs. For a
longitudinal wave such as sound wave, wavelength is the distance between adjacent compressions or
rarefaction.
c) Speed of sound
For a periodic wave, the shape of the string at any instant is a repeating pattern. The length of one
complete wave pattern is the distance from one crest to the next or from one trough to the next or
from any point to the corresponding point on the next repetition of the wave shape. We call this
distance the wavelength of the wave, denoted by the Greek letter lambda (λ).
The wave pattern travels with constant speed and advances a distance of one wavelength in a time
interval of one period T. So the wave speed is given by
fT
v , (1.01)
where f is the frequency of the wave.
Sound travels faster in liquids and solids than in gases, since the particles in liquids and solids are
closer together and can respond more quickly to the motion of their neighbors. As examples, the
speed of sound is 331 m/s in air, 1500 m/s in water and 5000 m/s in iron (though these can change
depending on temperature and pressure). Sound does not travel in vacuum.
Example 1.1 Wavelength of a musical sound
5
1. Sound waves can propagate in air. The speed of the sound depends on temperature of the air;
at C020 it is sm /344 . What is the wavelength of a sound wave in air if the frequency is 262 Hz
(the approximate frequency of middle C on a piano)?
Answer
Using Equation of wave (1.01): l =v
f=
344m / s
262Hz=1.31m
Factors which affect the velocity of sound in air
The speed of sound waves in a medium depends on the compressibility and density of the
medium. If the medium is a liquid or a gas and has a bulk modulus B and density , the speed of
sound waves in that medium is given by:
(1.02)
It is interesting to compare this expression with the equation applicable to transverse waves
on a string. In both cases, the wave speed depends on an elastic property of the medium (bulk
modulus B or tension in the string T) and on an inertial property of the medium (the density or
linear mass ).
In fact, the speed of all mechanical waves follows an expression of the general form
(1.03)
For longitudinal sound waves in a solid rod of material, for example, the speed of sound depends on
Young’s modulus Y and the density
Changes of pressure have no effect on the velocity of sound in air. Sir Isaac Newton showed
that:
(1.04)
In accordance with Boyle’s law, if the pressure of a fixed mass of air is doubled, the volume will
be halved. Hence the density will be doubled. Thus at constant temperature, the ratio will
always remain constant no matter how the pressure may change.
The speed of sound increases with temperature
If the air temperature increases at constant pressure the air will expand according to Charles’ law,
and therefore become less dense.
Bv
Tv
propertyinertia
propertyelasticv
Pv
P
6
The ratio will therefore increase, and hence the speed of sound increases with temperature.
For sound traveling through air, the relationship between wave speed and medium temperature is
, (1.05)
where smv /3310 is the speed of sound in air (at 0 degree Celsius and normal pressure) .
The speed of sound in air at standard temperature and pressure (25 oC, 760 mm of mercury) is
343 m/s. It is determined by how often the air molecules collide. The speed of sound increases by
about 6 m/s if the temperature increases by 10 oC (Glencoe, 2005).
Example 1.2
1. Find the speed of sound in water, which has a bulk modulus of at a
temperature of 0 °C and a density of .
Answer
Using equation (1.02), we find that
v =B
r=
2.1x109N /m2
1.00x103kg /m3=1.4km / s
P
0
0T
Tvv
29 /101.2 mNB 33 /1000.1 mkg
7
In general, sound waves travel more slowly in liquids than in solids because liquids are more
compressible than solids.
c) Amplitude
The amplitude of a wave is the maximum displacement of the medium from its rest position. The
amplitude of a transverse wave is the distance from the rest position to a crest or a trough. The more
energy a wave has, the greater is its amplitude.
1.1.3 Checking my progress
1. The correct statement about sound waves is that:
A. They are transverse waves
B. They can be polarized
C. They require material medium to propagate
2. Sound travels in
A. Air C. Water
B. Iron D. All of these
3. Two men talk on the moon. Assuming that the thin layer of gases on the moon is negligible, which
of the following is the right answer:
A. They hear each other with lower frequency
B. They hear each other with higher frequency
C. They can hear each other at such frequency
D. They cannot hear each other at all
4. Do you expect an echo to return to you more quickly on a hot day or a cold day?
A. Hot day.
B. Cold day.
C. Same on both days.
5. A sound wave is different than a light wave in that a sound wave is:
A. produced by an oscillating object and a light wave is not.
B. not capable of traveling through a vacuum.
C. not capable of diffracting and a light wave is.
D. capable of existing with a variety of frequencies and a light wave has a single frequency.
6. A spider of mass 0.30 g waits in its web of negligible mass see Fig. below. A slight movement
causes the web to vibrate with a frequency of about 15 Hz.
8
Fig.1. 3 A spider of mass waits in its web
(a) Estimate the value of the spring stiffness constant k for the web assuming simple harmonic
motion.
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.10 g were trapped
in addition to the spider?
9
1.2 PRODUCTION OF STATIONARY SOUND WAVES
Activity 1.3: Production of stationary sound waves.
Look at the Fig.1.4 of guitarist and then answer the following
question.
1. How do vibrations cause sound?
2. What determines the particular frequencies of sound produced
by an organ or a flute?
3. How resonance occurs in musical instruments?
4. How to describe what happens when two sound waves of
slightly different frequencies are combined?
1.2.1 Sound in pipes
The source of any sound is vibrating object. Almost any object can vibrate and hence be a source of
sound. For musical instruments, the source is set into vibration by striking, plucking, bowing, or
blowing. Standing waves (also known as stationary waves are superposition of two waves moving in
opposite directions, each having the same amplitude and frequency) are produced and the source
vibrates at its natural resonant frequencies. The most widely used instruments that produce sound
waves make use of vibrating strings, such as the violin, guitar, and piano or make use of vibrating
columns of air, such as the flute, trumpet, and pipe organ. They are called wind instruments.
We can create a standing wave:
in a tube, which is open on both ends. The open end of a tube is approximately a node in the
pressure (or an antinode in the longitudinal displacement).
in a tube, which is open on one end and closed on the other end. The closed end of a tube is
an antinode in the pressure (or a node in the longitudinal displacement).
In both cases a pressure node is always a displacement antinode and vice versa.
a. Tube of length L with two open ends
An open pipe is one which is open at both ends. The length of the pipe is the distance between
consecutive antinodes. But the distance between consecutive antinode is i.e.
(1.06)
The longest standing wave in a tube of length L with two open ends has displacement antinodes
(pressure nodes) at both ends. It is called the fundamental.
2
2L
L
vfLL
22
20
Fig.1. 4: A guitarist.
10
Fig.1. 5: Fundamental note (1st harmonic).
Notes with higher frequencies than fundamental can be obtained from the pipe by blowing harder.
The stationary wave in the open pipe has always an antinode at each end.
The next longest standing wave in a tube of length L with two open ends is the second harmonic
(first overtone). It also has displacement antinodes at each end.
Fig.1. 6: First overtone (second harmonic).
The second overtone is obtained from Fig. 1.6 and is the third harmonic.
Fig.1. 7: Second overtone (third harmonic).
An integer number of half wavelength has to fit into the tube of length L:
(1.07)
For a tube with two open ends, all frequencies with n equal to an integer are natural
frequencies.
The frequency f of fundamental note emitted by a vibrating string of length L, mass per unit length m
and under tension T is given by
(1.08)
Example 1.3
01 2 fL
vfL
02 32
3
3
2
2
3f
L
vf
LL
012
2
2nf
L
nvf
n
LnL n
01 nffn
T
Lf
2
1
11
1. The fundamental frequency of a pipe that is open at both ends is 594 Hz.
(a) How long is this pipe?
(b) Find the wavelength. Assume the temperature is C020
(c) Determine the fundamental frequency of the flute when all holes are covered and the
temperature is 10 °C instead of 20 °C?
Answer
(a) Length of the pipe: L =v
2 f0
=343m / s
2´594Hz= 0.29m
(b) The wavelength: mL 58.02
Quick check 1.1: Standing sound waves are produced in a pipe that is 1.20 m long. For the
fundamental and first two overtones, determine the locations along the pipe (measured from the left
end) of the displacement nodes and the pressure nodes if the pipe is open at both ends.
b. Tube of length L with one open end and one closed end.
The longest standing wave in a tube of length L with one open end and one closed end has a
displacement antinode at the open end and a displacement node at the closed end. This is the
fundamental.
L
vfLL
44
40
(1.09)
Fig.1. 8: Fundamental note (1st harmonic).
The next longest standing wave in a tube of length in a tube of length L with one open end and one
closed end is the third harmonic (second overtone). It also has a displacement antinode at one end
and a node at the other.
01 34
3
3
4
4
3f
L
vf
LL
(1.10)
12
Fig.1. 9: First overtone (third harmonic)
The next longest standing wave in a tube of length L with one open end and one closed end is the
second overtone (fifth harmonic).
02 54
5
5
4
4
5f
L
vf
LL
(1.11)
Fig.1. 10: Second overtone (fifth harmonic)
An odd-integer number of quarter wavelength has to fit into the tube of length L.
(1.12)
For a tube with one open end and one closed end, frequencies on fnL
vnf )12(
4
)12(
, with n
equal to an odd integer are natural frequencies. Only odd harmonics of the fundamental are natural
frequencies.
Another way to analyze the vibrations in a uniform tube is to consider a description in terms of the
pressure in the air. Where the air in a wave is compressed, the pressure is higher, whereas in a wave
expansion (or rarefaction), the pressure is less than normal. We call a region of increased density a
compression; a region of reduced density is a rarefaction.
The wavelength is the distance from one compression to the next or from one rarefaction to the next.
0)12(4
)12(
12
4
4
)12(fn
L
vnf
n
LnL n
13
Fig.1. 11: Pressure variation in the air: Graphs of the three simplest modes of vibration (standing waves) for a
uniform tube open at both ends (“open tube”).
The open end of a tube is open to the atmosphere. Hence the pressure variation at an open end must
be a node: the pressure does not alternate, but remains at the outside atmospheric pressure as shown
in Fig.1.12.
Fig.1. 12Modes of vibration (standing waves) for a tube closed at one end (“closed tube”).
If a tube has a closed end, the pressure at that closed end can readily alternate to be above or below
atmospheric pressure. Hence there is a pressure antinode at a closed end of a tube. There can be
pressure nodes and antinodes within the tube as shown in Fig.1.12.
14
Example 1.4
1. A section of drainage culvert 1.23 m in length makes a howling noise when the wind blows.
(a) Determine the frequencies of the first three harmonics of the culvert if it is open at both
ends. Take v = 343 m/s as the speed of sound in air.
(b) What are the three lowest natural frequencies of the culvert if it is blocked at one end?
(c) For the culvert open at both ends, how many of the harmonics present fall within the normal
human hearing range (20 Hz to 17 000 Hz)?
Answer
a) The frequency of the first harmonic of a pipe open at both ends is
f =v
2L=
343m / s
2x1.23m=139Hz
Because both ends are open, all harmonics are present; thus,
f2= 2 f
1= 2x139Hz = 278Hz
and f3= 3 f
1= 3x139Hz = 417Hz
b) The fundamental frequency of a pipe closed at one end is
f =v
4L=
343m / s
4x1.23m= 69.7Hz
In this case, only odd harmonics are present; hence, the next two harmonics have frequencies
f3= 3 f
1= 3x69.7Hz = 209Hz
and f5= 5 f
1= 5x69.7Hz = 349Hz
c) Because all harmonics are present, we can express the frequency of the highest harmonic heard
as where n is the number of harmonics that we can hear.
For , we find that the number of harmonics present in the audible range is
Only the first few harmonics are of sufficient amplitude to be heard.
Quick check 1.2: Standing sound waves are produced in a pipe that is 1.20 m long. For the
fundamental and first two overtones, determine the locations along the pipe (measured from the left
end) of the displacement nodes and the pressure nodes if the pipe is closed at the left end and open at
the right end.
1.2.2 Vibrating strings
The string is a tightly stretched wire or length of gut. When it is struck, bowed or plucked,
progressive transverse waves travel to both ends, which are fixed, where they are reflected to meet
1nffn
Hzfn 17000
122139
17000n
15
the incident waves. A stationary wave pattern is formed for waves whose wavelengths fit into the
length of the string, i.e. resonance occurs.
If you shake one end of a cord (slinky) and the other end is kept fixed, a continuous wave will travel
down to the fixed end and be reflected back, inverted. The frequencies at which standing waves are
produced are the natural frequencies or resonant frequencies of the cord. A progressive sound wave
(i.e. a longitudinal wave) is produced in the surrounding air with frequency equal to that of the
stationary transverse wave on the string.
Now let consider a cord stretched between two supports that is plucked like a guitar or violin string.
Waves of a great variety of frequencies will travel in both directions along the string, will be
reflected at the ends, and will be travel back in the opposite direction. The ends of the string, since
they are fixed, will be nodes.
The lowest frequency, called the fundamental frequency, corresponds to one antinode (or loop) and
corresponds to whole length of the string i.e. , the other natural frequencies are called
overtones or harmonics. The next mode after the fundamental has two loops and is called the
second harmonic or first overtone and so on.
Fundamental note (first harmonic): (1.13)
The frequency (1.14)
It was stated that the speed of a transverse wave travelling along a string is given by
The frequency of the vibration is given by: (1.15)
First overtone (second harmonic) of a string plucked in the middle corresponds to a stationary wave
which has nodes at the fixed ends and antinode in the middle. If is the wave length it can be seen
that:
(1.16)
The frequency of fist overtone is given by:
(1.17)
In order to find the frequency f of each vibration we use equation: and we see that
(1.18)
where and
2L
2L
2
v vf f
L
Tv
1
2
Tf
L
1
1 1
3 2
2 3
ll
1
1
3
2
c Tf
cf
1n
n
vf nf
Tv
1
1
2
Tf
L
16
Consider a string of length L fixed at both ends, as shown in Fig.1.12. Standing waves are set up in
the string by a continuous superposition of wave incident on and reflected from the ends.
Note that there is a boundary condition for the waves on the string. The ends of the string, because
they are fixed, must necessarily have zero displacement and are, therefore, nodes by definition
Fig.1. 13: Fundamental and first two overtones: (a) A string of length L fixed at both ends. The normal modes of
vibration form a harmonic series: (b) the fundamental note (first harmonic); (c) First overtone (second harmonic);
(d) the second overtone (third harmonic) (Halliday, Resneck, & Walker, 2007).
Example 1.5
1: A piano string is 1.10 m long and has mass of 9 g.
a) How much tension must the string be under if it is to vibrate at a fundamental frequency of
131 Hz?
b) What are the frequencies of the first four harmonics?
Answer
a) The wavelength of the fundamental frequency is
The velocity is then v = l f = (2.2m)x(131Hz) = 278m / s
Then from
b) The frequencies of second, third, and fourth harmonics are three, and four times the fundamental
frequency: 262 Hz, 393 Hz, and 524 Hz.
Quick check 1.3: Middle C on a piano has a fundamental frequency of 262 Hz, and the first A above
middle C has a fundamental frequency of 440 Hz.
a) Calculate the frequencies of the next two harmonics of the C string.
2 2.20L m
NL
mvT
m
TLv
Tv 679
22
17
b) If the A and C strings have the same linear mass density and length L, determine the ratio of
tensions in the two strings.
c) With respect to a real piano, the assumption we made in (b) is only partially true. The string
densities are equal, but the length of the A string is only 64 % of the length of the C string. What
is the ratio of their tensions?
1.2.3. Wave Interference and Superposition
a. Wave interference
Up to this point we’ve been discussing waves that propagate continuously in the same direction. But
when a wave strikes the boundaries of its medium, all or part of the wave is reflected. When you yell
at a building wall or a cliff face some distance away, the sound wave is reflected from the rigid
surface and you hear an echo. When you flip the end of a rope whose far end is tied to a rigid
support, a pulse travels the length of the rope and is reflected back to you. In both cases, the initial
and reflected waves overlap in the same region of the medium. This overlapping of waves is called
interference.
In general, the term “interference” refers to what happens when two or more waves pass through the
same region at the same time Fig.1.14 shows an example of another type of interference that involves
waves that spread out in space.
Fig.1. 14: Two speakers driven by the same amplifier: Constructive interference occurs at point P and destructive
interference occurs at Q.
Two speakers, driven in phase by the same amplifier, emit identical sinusoidal sound waves with the
same constant frequency. We place a microphone at point P in the figure, equidistant from the
speakers. Wave crests emitted from the two speakers at the same time travel equal distances and
arrive at point P at the same time; hence the waves arrive in phase, and there is constructive
interference.
The total wave amplitude at P is twice the amplitude from each individual wave, and we can measure
this combined amplitude with the microphone.
Now let’s move the microphone to point Q, where the distances from the two speakers to the
microphone differ by a half-wavelength. Then the two waves arrive a half-cycle out of step, or out of
phase; a positive crest from one speaker arrives at the same time as a negative crest from the other.
Destructive interference takes place, and the amplitude measured by the microphone is much smaller
18
than when only one speaker is present. If the amplitudes from the two speakers are equal, the two
waves cancel each other out completely at point Q, and the total amplitude there is zero.
b. The principle of superposition
Combining the displacements of the separate pulses at each point to obtain the actual displacement is
an example of the principle of superposition: “When two waves overlap, the actual displacement of
any point on the string at any time is obtained by adding the displacement the point would have if
only the first wave were present and the displacement it would have if only the second wave were
present”.
In other words, the wave function ),( xty that describes the resulting motion in this situation is
obtained by adding the two wave functions for the two separate waves:
),(),(),( 21 xtyxtyxty (1.19)
Where )sin(),( 11 kxtAxty and )sin(),( 12 kxtAxty
These waves overlap and interfere. The resultant wave as these waves overlap and interfere can write
as)
2
)(sin(
2cos2),(),().( 1212
21
kxtAxtyxtyxty (1.20)
As we saw with transverse waves, when two waves meet they create a third wave that is a
combination of the other two waves. This third wave is actually the sum of the two waves at the
points where they meet. The two original waves are still there and will continue along their paths
after passing through each other. After passing the third wave no longer exists.
Its amplitude is the magnitude
2
cos2 12 AAr
(1.21)
Activity 1.4:
Problem 1
The Adventures of Marvin the Mouse: You and your friend are walking down by the pool when
you hear a cry for help. Poor Marvin the Mouse has fallen into the pool and needs your help. The
sides of the pool are to slippery for Marvin to climb out but there is an inner tube anchored in the
center of the pool. Oh no! The sides of the inner tube are too slippery and high for Marvin to climb.
He's getting tired and can't swim to the sides; he has just enough energy to float by the inner tube.
Having studied about waves, you and your friend take up positions on opposite sides of the pool.
How did you help Marvin get safely onto the inner tube?
Problem 2: Dance club designer
You are the designer of a new Dance Club. You have been informed that you need to design the club
in such a way that the telephone is placed in a location that allows the customers to hear the people
on the other side. The phone company states that they can only put the phone line in at a point 20 m
from the stage. Develop a model which allows the customers to use the phone with the least amount
19
of trouble given that the phone must be placed at a distance of 20 m, (2/3 the room size), from the
stage. This will be an area where there will be virtually no sound.
c. Resonance of sound
We have seen that a system such as a taut string is capable of oscillating in one or more normal
modes of oscillation. If a periodic force is applied to such a system, the amplitude of the resulting
motion is greater than normal when the frequency of the applied force is equal to or nearly equal to
one of the natural frequencies of the system. This phenomenon is known as resonance. Although a
block–spring system or a simple pendulum has only one natural frequency, standing-wave systems
can have a whole set of natural frequencies.
Because oscillating systems exhibits large amplitude when driven at any of its natural frequencies,
these frequencies are often referred to as resonance frequencies. Fig.1.15 shows the response of an
oscillating system to various driving frequencies, where one of the resonance frequencies of the
system is denoted by f0
Fig.1. 15: Graph of the amplitude versus driving frequency for oscillating system. The amplitude is a maximum at
the resonance frequency. Note that the curve is not symmetric (Halliday, Resneck, & Walker, 2007)
One of our best models of resonance in a musical instrument is a resonance tube. This is a hollow
cylindrical tube partially filled with water and forced into vibration by a tuning fork (Fig.1.16). The
tuning fork is the object that forced the air, inside the resonance tube, into resonance.
Fig.1. 166: Turning fork forcing air column into resonance
20
As the tines of the tuning fork vibrate at their own natural frequency, they created sound waves that
impinge upon the opening of the resonance tube. These impinging sound waves produced by the
tuning fork force air inside of the resonance tube to vibrate at the same frequency. Yet, in the
absence of resonance, the sound of these vibrations is not loud enough to discern.
Resonance only occurs when the first object is vibrating at the natural frequency of the second
object. So if the frequency at which the tuning fork vibrates is not identical to one of the natural
frequencies of the air column inside the resonance tube, resonance will not occur and the two objects
will not sound out together with a loud sound. But the location of the water level can be altered by
raising and lowering a reservoir of water, thus decreasing or increasing the length of the air column.
So by raising and lowering the water level, the natural frequency of the air in the tube could be
matched to the frequency at which the tuning fork vibrates.
When the match is achieved, the tuning fork forces the air column inside of the resonance tube to
vibrate at its own natural frequency and resonance is achieved. The result of resonance is always a
big vibration - that is, a loud sound.
A more spectacular example is a singer breaking a wine glass with her amplified voice. A good-
quality wine glass has normal-mode frequencies that you can hear by tapping it.
If the singer emits a loud note with a frequency corresponding exactly to one of these normal-mode
frequencies, large-amplitude oscillations can build up and break the glass (Fig. 1.18)
Fig.1. 17: Some singers can shatter a wine glass by maintaining a certain frequency of their voice for seconds, (a)
Standing-wave pattern in a vibrating wine glass. (b) A wine glass shattered by the amplified sound of a human
voice
c. Beats and its phenomena
Beats occur when two sounds-say, two tuning forks- have nearly, but not exactly, the same
frequencies interfere with each other. A crest may meet a trough at one instant in time resulting in
destructive interference. However at later time the crest may meet a crest at the same point resulting
in constructive interference. To see how beats arise, consider two sound waves of equalamplitudes
and slightly different frequencies as shown on the figure below.
21
Fig.1. 188: Beats occur as a result of the superposition of two sound waves of slightly different frequencies (Cutnell
& Johnson, 2006).
In 1.00 s, the first source makes 50 vibrations whereas the second makes 60. We now examine the
waves at one point in space equidistant from the two sources. The waveforms for each wave as a
function of time, at a fixed position, are shown on the top graph of Fig. 1.19; the red line represents
the 50 Hz wave, and the blue line represents the 60 Hz wave. The lower graph in Fig. 1.18 shows the
sum of the two waves as a function of time. At the time the two waves are in phase they interfere
constructively and at other time the two waves are completely out of phase and interfere
destructively. Thus the resultant amplitude is large every 0.10 s and drops periodically in between.
This rising and falling of the intensity is what is heard as beats. In this case the beats are 0.10 s apart.
The beat frequency is equal to the difference in frequencies of the two interfering waves..
Consider two sound waves of equal amplitude traveling through a medium with slightly different
frequencies f1 and f2atchosen point x = 0:
and
Using the superposition principle, we find that the resultant wave function at this point is
The trigonometric identity allows us to write the expression
for y as
We see that the resultant sound for a listener standing at any given point has an effective frequency
equal to the average frequency and amplitude given by the expression:
(1.22)
tfAy 11 2cos tfAy 22 2cos
)2cos2(cos 2121 tftfAyyy
)2
cos()2
cos(2coscosbaba
ba
tff
tff
Ayyy )2
(2cos)2
(2cos2 212121
2
21 ff
tff
AA )2
(2cos2 21max
22
The frequency of the beats is equal to the difference in the frequencies of the two sound waves:
(1.23)
The interference pattern varies in such a way that a listener hears an alternation between loudness
and softness. The variation from soft to loud and back to soft is called a Beat. The phenomena of
beats can be used to measure the unknown frequency of a note.
Example 1.6
1. Two identical piano strings of length 0.750 m are each tuned exactly to 440 Hz. The tension in
one of the strings is then increased by 1.0%. If they are now struck, what is the beat frequency
between the fundamentals of the two strings?
Answer:
We find the ratio of frequencies if the tension in one string is 1.0% larger than the other:
Thus, the frequency of the tightened string is
and the beat frequency is
Quick check 1.4: A tuning fork produces a steady 400 Hz tone. When this tuning fork is struck and
held near a vibrating guitar string, twenty beats are counted in five seconds. What are the possible
frequencies produced by the guitar string?
1.2.4 Checking my progress
1. Is the wavelength of the fundamental standing wave in a tube open at both ends greater than, equal
to, or less than the wavelength of the fundamental standing wave in a tube with one open end and
one closed end?
2. You blow across the opening of a bottle to produce a sound. What must be the approximate height
of the bottle for the fundamental note to be a middle C (1.29 m)?
3. Two loudspeakers are separated by 2.5 m. A person stands at 3.0 m from one and at 3.5 m from
the other one. Assume a sound velocity of 343 m/s.
a) What is the minimum frequency to present destructive interference at this point?
b) Calculate the other two frequencies that also produce destructive interference.
4. How would you create a longitudinal wave in a stretched spring? Would it be possible to create a
transverse wave in a spring?
5. In mechanics, massless strings are often assumed. Why is this not a good assumption when
discussing waves on strings?
1 2beat frequency frequency of loud sound heard f f
005.1010.1
2
2
1
1
1
2
1
2
1
2
1
2
1
2 T
T
T
T
T
T
v
v
L
vL
v
f
f
Hzff 442440005.1005.1 12
Hzfbeat 2440442
23
6. Draw the second harmonic (The second lowest tone it can make.) of a one end fixed, one end open
pipe. Calculate the frequency of this mode if the pipe is 53.2 cm long, and the speed of sound in the
pipe is 317 m/s.
7. Calculate the wavelengths below. The length given is the length of the waveform (The picture)
L = 45 cm L = 2.67 m L = 68 cm
8. A guitar string is 64 cm long and has a fundamental Mi frequency of 330 Hz. When pressing in the
first fret (nearest to the tuning keys) see fig. the string is shortened in such a way that it plays a Fa
note having a frequency of 350 Hz. Calculate the distance between this first fret and the nut
necessary to get this effect.
9. Why is a pulse on a string considered to be transverse?
10. A guitar string has a total length of 90 cm and a mass of 3.6 g. From the bridge to the nut there is
a distance of 60 cm and the string has a tension of 520 N. Calculate the fundamental frequency and
the first two overtones
24
1.3 CHARACTERISTICS OF MUSICAL NOTES
Activity 1.5: Characteristics of musical notes
The physical characteristics of a sound wave are directly related to the perception of that sound by a
listener. Before you read this section answer these questions. As you read this section answer again
these questions. Compare your answer.
1. What is the difference between the sound of whistle and that of drum?
2. Can you tell which musical instrument is played if the same note is played on different
instrument without seeing it? Explain
3. How can you calculate the intensity of a sound wave?
A musical note is produced by vibrations that are regular and repeating, i.e. by periodic motion.
Non-periodic motion results in noise which is not pleasant to the ear. Many behaviors of musical
note can be explained using a few characteristics: intensity and loudness, frequency and pitch, and
quality or timber
1.3.1. Pitch and frequency
The sound of a whistle is different from the sound of a drum. The whistle makes a high sound. The
drum makes a low sound. The highness or lowness of a sound is called its pitch. The higher the
frequency, the higher is the pitch. The frequency of an audible sound wave determines how high or
low we perceive the sound to be, which is known as pitch.
Frequency refers to how often something happens or in our case, the number of periodic,
compression-rarefaction cycles that occur each second as a sound wave moves through a medium --
and is measured in Hertz (Hz) or cycles/second. The term pitch is used to describe our perception of
frequencies within the range of human hearing.
If a note of frequency 300 Hz and note of 600 Hz, are sounded by a siren, the pitch of the higher note
is recognized to be an upper octave of the lower note. The musical interval between two notes is an
upper octave if the ratio of their frequencies is 2:1. It can be shown that the musical interval
between two notes depends on the ratio of their frequencies, and not on the actual frequencies.
Whether a sound is high-pitched or low-pitched depends on how fast something vibrates. Fast
vibrations make high-pitched sounds. Slow vibrations make low-pitched sounds.
Do not confuse the term pitch with frequency. Frequency is the physical measurement of the
number of oscillations per second. Pitch is a psychological reaction to sound that enables a person to
place the sound on a scale from high to low, or from treble to bass. Thus, frequency is the stimulus
and pitch is the response. Although pitch is related mostly to frequency, they are not the same. A
phrase such as “the pitch of the sound” is incorrect because pitch is not a physical property of the
sound.The octave is a measure of musical frequency.
1.3.2 Intensity and amplitude
A police siren makes a loud sound. Whispering makes a soft sound. Whether a sound is loud or soft
depends on the force or power of the sound wave. Powerful sound waves travel farther than weak
25
sound waves. To talk to a friend across the street you have to shout and send out powerful sound
waves. Your friend would never hear you if you whispered.
A unit called the decibel measures the power of sound waves. The sound waves of a whisper are
about 10 decibels. Loud music can have a level of 120 decibels or more. Sounds above 140 decibels
can actually make your ears hurt. The energy carried by a sound wave is proportional to the square of
its amplitude. The energy passing a unit area per unit time is called the intensity of the wave.
The intensity of spherical sound wave at a place p is defined as the energy per second per m2, or
power per m2 flowing normally through an area at X. i.e
24
/
r
P
A
tEI
(1.25)
So the unit of intensity is
where r is the distance from the source for a spherical wave
Example 1.7
1. If the intensity of an earth-quake P wave 100 km from the source is , what
is the intensity 400 km from the source?
Answer
Power:
Sound intensity level
To the human ear the change in loudness when the power of a sound increases from 0.1 W to 1.0 W
is the same as when 1 W to 10 W. The ear responds to the ratio of the power and not to their
difference.
We measure sound level intensity in terms of "decibels". The unit bel is named after the inventor of
the telephone, Alexander Graham Bell (1847–1922). The decibel is a "relative unit" which is actually
dimensionless, comparing a given sound to a standard intensity which represents the smallest audible
sound:
(1.26)
Where 212
0 /10 mWI at 1000 Hz is the reference intensity. 0 dB thus represents the softest
audible sound (threshold of human hearing), while 80 dB (i.e., moderately loud music) represents an
intensity which is one hundred million times greater.
Example 1.8
1. Two identical machines are positioned the same distance from a worker. The intensity of sound
delivered by each machine at the location of the worker is . Find the sound level
heard by the worker (a) when one machine is operating and (b) when both machines are operating.
2/W m
6 21.0 10 /I W m
22 2 4 21
1 1 2 2 2 1 2
2
4 4 6.2 10 /r
P I r I r I I W mr
oI
Ilog10
27 /100.2 mW
26
Answer
(a) The sound level at the location of the worker with one machine operating is
b1=10log
2.0´10-7W /m2
1.00´10-12W /m2= 53dB
(b) When both machines are operating, the intensity is doubled to ; therefore, the
sound level now is b2
=10log4.0´10-7W /m2
1.00´10-12W /m2= 56 dB
From these results, we see that when the intensity is doubled, the sound level increases by only
3 dB.
Quick check 1.4: A point source emits sound waves with an average power output of 80.0 W.
(A) Find the intensity 3.00 m from the source.
(B) Find the distance at which the sound level is 40 dB.
Activity 1.6: Noise or music
Most people like to listen to music, but hardly anyone likes to listen to noise.
1. What is the physical difference between musical sound and noise?
2. What is the effect of noise to human being?
The physical characteristics of a sound wave are directly related to the perception of that sound by a
listener. For a given frequency the greater the pressure amplitude of a sinusoidal sound wave, the
greater the perceived loudness.
The loudness or softness of sound depends on the intensity of the sound wave reaching the person
concerned. Loudness is a subjective quantity unlike intensity. Sound that is not wanted or unpleasant
to the ear is called noise. High intensity can damage hearing.The higher the intensity, the louder is
the sound. Our ears, however, do not respond linearly to the intensity. A wave that carries twice the
energy does not sound twice as loud.
1.3.3 Quality or timbre
If the same note is sounded on the violin and then on the piano, an untrained listener can tell which
instrument is being used, without seeing it. We would never mistake a piano for flute. We say that
the quality or timbre of note is different in each case. The manner in which an instrument is played
strongly influences the sound quality.
Two tones produced by different instruments might have the same fundamental frequency (and thus
the same pitch) but sound different because of different harmonic content. The difference in sound is
called tone color, quality, or timbre. A violin has a different timbre than a piano.
27 /100.4 mW
27
1.3.4 Checking my progress
1. Complete each of the following sentences by choosing the correct term from the word bank:
loudness, pitch, sound quality, echoes, intensity and noise
a) The ------------ of a sound wave depends on its amplitude
b) Reflected sound waves are called ---------------------------
c) Two different instruments playing the same note sound different because of ------------------
2. Plane sound wave of frequency 100 Hz fall normally on a smooth wall. At what distances from the
wall will the air particles have:
a. Maximum
b. Minimum amplitude of vibration?
Give reasons for your answer. The speed of sound in air may be taken as 340 m/s
3. A boy whistles a sound with the power of W4105.0 . What will be his sound intensity at a
distance of 5m?
4. Calculate the intensity level equivalent to an intensity 1 nW/m2
5. If the statement is true, write true. If it is false, change the underlined word or words to make the
statement true.
a. Intensity is mass per unit volume.
b. Loudness is how the ear perceives frequency
c. Music is a set of notes that are pleasing
28
1.4 APPLICATIONS OF SOUND WAVES
Activity1.7: Doppler Effect and uses of sound waves
1. Why does the pitch of a siren change as it moves past you?
2. How is Doppler’s effect used in communication with satellites?
3. Explain how is the Doppler’s effect used in Astronomy?
4. People use sound for other things other than talking and making music. In your own word, give
more examples and explanations to support this statement.
1.4.1 The Doppler Effect
Doppler’s effect is the apparent variation in frequency of a wave due to the relative motion of the
source of the wave and the observer.
The effect takes its name from the Austrian Mathematician Christian Johann
Doppler (1803-1853), who first stated the physical principle in 1842.
Doppler's principle explains why, if a source of sound of a constant pitch is
moving toward an observer, the sound seems higher in pitch, whereas if the
source is moving away it seems lower. This change in pitch can be heard by
an observer listening to the whistle of an express train from a station
platform or another train.
Fig.1. 20: An observer O (the cyclist) moves with a speed vO toward a stationary point source S, the horn of a
parked truck. The observer hears a frequency f’ that is greater than the source frequency.
a. When the source of the wave approaches detector (observer) at speed vs,
The wavelength is shortened by an amount , where T is the period of the wave. This is simply
due to the motion of the source. Since the "received" wavelength (𝜆𝑟) is related to the "source"
wavelength (𝜆𝑠) by
𝜆𝑟 = 𝜆𝑠 − 𝑣𝑠𝑇 = 𝜆𝑠𝑐−𝑣𝑠
𝑐 (1.26)
sv T
Fig.1. 19 C.J. Doppler
(Douglass, PHYSICS,
Principles with
applications., 2014)
29
Knowing the velocity of the moving source of wave ( ), you can use the equation fv to convert
the wavelength equations to solve for frequency.
The received frequency is related to the source frequency by
𝑓𝑟 = 𝑓𝑠𝑐
𝑐−𝑣𝑠 (1.27)
Hence the frequency you hear is higher than the frequency emitted by the approaching source.
Example 1.9
1. If a source emits a sound of frequency 400 Hz when at rest, then when the source moves toward
a fixed observer with a speed of 30 m/s, what frequency does the observer hears knowing that the
speed of a sound in air at room temperature is 343m/s?
Answer
The observer hears a frequency of𝑓𝑟 = 400343
343−30= 438𝐻𝑧
As the source passes you and recedes, the "speed of approach" vs becomes negative, and the
frequency you hear becomes lower than the frequency emitted by the now receding source.
The frequency of the wave will be: s
srvv
vff
(1.28)
In this case if a source vibrating at 400 Hz is moving away from a fixed observer at 30 m/s, the later
will hear a frequency of about𝑓𝑟 = 400343
343+30= 434𝐻𝑧
b. When the source is stationary but you are approaching it at a speed vo.
The Doppler’s effect also occurs when the source is at rest and the observer is in motion. If the
observer is travelling toward the source the pitch is higher; and if the observer is travelling away
from the source, the pitch is lower.
With a fixed source and moving observer, the distance between wave crests, the wavelength , is not
changed. But the velocity of the crests with respect to the observer is changed. If the observer is
moving toward the source, the speed of the wave relative to the observer is 0vvv
Hence, the new frequency is𝑓𝑟 = 𝑓𝑠𝑐+𝑣𝑜
𝑐 (1.29)
If the observer is moving away from the source, the relative velocity is ovvv ' and
𝑓𝑟 = 𝑓𝑠𝑐−𝑣𝑜
𝑐 (1.30)
sv
30
Example 1.10
1. The siren of a police car at rest emits at a predominant frequency of 1600 Hz. What frequency
will be heard if you were moving with speed of 25 m/s?
a) Toward it?
b) Away from it?
Answer
a) We use equation 𝑓𝑟 = 1600343+25
343= 1716.6𝐻𝑧
b) We use equation: 𝑓𝑟 = 1600343−25
343= 1483𝐻𝑧
c. If both the source and receiver are moving
If both the source and receiver are moving and vs and vr are the speeds with which they are
approaching each other (respectively), the Doppler shift is
𝑓𝑟 = 𝑓𝑜𝑐+𝑣𝑜
𝑐−𝑣𝑠 (1.31)
Here v is the speed of sound in air; is the speed of the listener (substituted as positive if he moves
towards the source, as negative if he moves away from the source), and is the speed of the source
(reckoned as positive if it moves towards the listener, as negative if it moves away from the listener.
Example 1.11
1. A car, sounding a horn producing a note of 500 Hz, approaches and passes a stationary observer
O at a steady speed of 20 m/s. Calculate the change in pitch of the note heard by O (speed of sound
is 340 m/s)
Answer:
Towards O, apparent frequency to O:
Away from O, the apparent frequency to O:
Change in pitch: .
For convenience, we can write Doppler’s effect equation as a single equation that covers all cases of
both source and observer in motion:
s
oor
vv
vvff
(1.32)
The upper signs apply if source and/or observer move toward each other. The lower signs apply if
they are moving apart. The word toward is associated with an increase in observed frequency. The
words away from are associated with a decrease in observed frequency.
rv
sv
340500 531
340 20f Hz
340500 472
340 20f Hz
0.9f
f
31
Although the Doppler’s effect is most typically experienced with sound waves, it is a phenomenon
that is common to all waves. For example, the relative motion of source and observer produces a
frequency shift in light waves. The Doppler’s effect is used in police radar systems to measure the
speeds of motor vehicles. Likewise, astronomers use the effect to determine the speeds of stars,
galaxies, and other celestial objects relative to the Earth.
Example 1.12
1: As an ambulance travels east down a highway at a speed of 33.5 m/s, its siren emits sound at a
frequency of 400 Hz. What frequency is heard by a person in a car traveling west at 54.6 m/s
(a) as the car approaches the ambulance and
(b) as the car moves away from the ambulance?
Answer
(a) As the ambulance and car approach each other, the person in the car hears the frequency
fr=v+ v
0
v- vs
fs=
343m / s+ 24.6m / s
343m / s-33.5m / sx400Hz = 475Hz
(b) As the vehicles recede from each other, the person hears the frequency
fr=v- v
0
v+ vs
fs=
343m / s- 24.6m / s
343m / s+33.5m / sx400Hz = 475Hz
The change in frequency detected by the person in the car is 475 Hz - 338 Hz = 137 Hz, which is
more than 30% of the true frequency.
c) Suppose the car is parked on the side of the highway as the ambulance speeds by. What
frequency does the person in the car hear as the ambulance (a) approaches and (b) recedes?
Answer
(a) 443 Hz. (b) 364 Hz.
The motion of the source of sound affects its pitch.
Quick check 1.5: Middle C on the musical scale has a frequency of 264 Hz. What is the wavelength
of the sound wave?
1.4.2 Uses of Ultrasonic
a) Echolocation
Some marine mammals, such as dolphin, whales, and porpoises use sound waves to locate distant
objects. In this process, called echolocation, a dolphin produces a rapid train of short sound pulses
that travel through the water, bounce off distant objects, and reflect back to the dolphin. From these
echoes, dolphins can determine the size, shape, speed, and distance of their potential prey.
Experiments have shown that at distance of 114 m, a blindfolded dolphin can locate a stainless-steel
32
sphere with a diameter of 7.5 cm and can distinguish between a sheet of aluminum and a sheet of
copper (Cutnell & Johnson, 2006).
The Ultrasonic waves emitted by a dolphin enable it to see through bodies of other animals and
people (Fig.1.20). Skin muscles and fat are almost transparent to dolphins, so they see only a thin
outline of the body but the bones, teeth and gas-filled cavities are clearly apparent. Physical
evidence of cancers, tumors, heat attacks, and even emotional shake can all be seen by dolphin. What
is more interesting, the dolphin can reproduce the sonic signals that paint the mental image of its
surroundings, and thus the dolphin probably communicates its experience to other dolphins. It needs
no words or symbol for fish, for example, but communicates an image of the real thing.
Fig.1. 21: The Ultrasonic waves emitted by a dolphin enable it to see through bodies of other animals and people.
Bats also use echo to navigate through air. Bats use ultrasonic with frequencies up to 100 kHz to
move around and hunt (Fig.1.23).
Fig.1. 22 Bats use ultrasonic with frequencies up to 100 kHz to move around and hunt.
The waves reflect off objects and return the bat’s ears. The time it takes for the sound waves to return
tells the bat how far it is from obstacles or prey. The bat uses the reflected sound waves to build up a
picture of what lies ahead.
Dogs, cats and mice can hear ultrasound frequencies up to 450 kHz.
Some animals not only hear ultrasound but also use ultrasonic to see in dark.
b) In medicine
The sonogram is device used in medicine and exploits the reflected ultrasound to create images. This
pulse-echo technique can be used to produce images of objects inside the body and is used by
Physicians to observe fetuses. Ultrasound use a high frequency in the range of 1 MHz to 10 MHz that
is directed into the body, and its reflections from boundaries or interfaces between organs and other
structures and lesions in the body are then detected. (Michael, Loannis, & Martha, 2006)
33
Tumors and other abnormal growths can be distinguished; the action of heart valves and the
development of a foetus (Fig.1.24) can be examined; and information about various organs of the
body, such as the brain, heart, liver, and kidneys, can be obtained.
Although ultrasound does not replace X-rays, for certain kinds of diagnosis it is more helpful. Some
tissues or fluid are not detected in X-ray photographs, but ultrasound waves are reflected from their
boundaries. Echoes from ultrasound waves can show what is inside the body. Echo is a reflection of
sound off the surface of an object.
Fig.1. 23: Ultrasound image as an example of using high-frequency sound waves to see within the human body
(Douglass, PHYSICS, Principles with applications., 2014).
In medicine, ultrasonic is used as a diagnostic tool, to destroy diseased tissue, and to repair damaged
tissue. Ultra sound examination of the heart is known as echocardiography.
c) Sonar
The sonar or pulse-echo technique is used to locate underwater objects and to determine distance. A
transmitter sends out a sound pulse through the water, and a detector receives its reflection, or echo,
a short time later. This time interval is carefully measured, and from it the distance to the reflecting
object can be determined since the speed of sound in water is known. The depth of the sea and the
location of sunken ships, submarines, or fish can be determined in this way. Sonar also tells how fast
and what direction things are moving. Scientists use sonar to make maps of the bottom of the sea.
An analysis of waves reflected from various structures and boundaries within the Earth reveals
characteristic patterns that are also useful in the exploration for oil and minerals.
Radar used at airports to track aircraft involves a similar pulse-echo technique except that it uses
electromagnetic (EM) waves, which, like visible light, travel with a speed of 3 ×108 m/s.
One reason for using ultrasound waves, other than the fact that they are inaudible, is that for shorter
wavelengths there is less diffraction so the beam spreads less and smaller objects can be detected.
1.4.3 Uses of infrasonic
Elephants use infrasonic sounds waves to communicate with one another. Their large ears enable
them to detect these low frequency sound waves which have relatively long wavelengths. Elephants
can effectively communicate in this way even when they are separated by many kilometers. Some
animals, such as this young bat-eared fox, have ears adapted for the detection of very weak sounds.
34
Fig.1. 24: Some animals, such as this young bat-eared fox, have ears adapted for the detection of very weak
sounds.
1.4.4 Checking my progress
For question 1 to 2: Choose the letter of the best answer
1. Choose the best answer: Bats can fly in the dark without hitting anything because
A. They are flying mammals C. They are guided by ultrasonic waves produced by them
B. Their night vision is going D. Of no scientific reason
2. Bats and dolphins use echolocation to determine distances and find prey. What characteristic of
sound waves is most important for echolocation?
A. sound waves reflect when they hit a surface C. sound waves diffract around corner
B. sound waves spread out from a source D. sound waves interfere when they overlap
3. Discuss application of sound waves in medicine and navigation
4. Explain how sonar is used to measure the depth of a sea
5. a) What is meant by Doppler Effect?
b. A police car sound a siren of 1000 Hz as it approaches a stationary observer at a speed of 33.5 m/s.
What is the apparent frequency of the siren as heard by the observer if the speed of sound in air is
340 m/s.
c. Give one application of the Doppler Effect.
35
1.5 END UNIT ASSESSMENT
1.5.1 Multiple choices question
For question 1 to 6, choose the letter of the best answer
1. Which of the following affects the frequency of wave?
A. Reflection
B. Doppler effect
C. Diffraction
D. All of the above
2. Consider the following statements:
I. Recording of sound on tapes was first invented by Valdemar Poulsen.
II. Audio tapes have magnetic property.
III. The tapes may also be made of PVC (Polyvinyl-chloride)
Of these statements:
A. I, II, and III all are correct. C. I and II are correct, III is wrong
B. I, II, and III all are wrong D. I and II are wrong, III is correct
3. Nodes are
A. Positions of maximum displacement
B. Positions of no displacement
C. A position between no displacement and maximum displacement
D. None of these
4. Sound waves are
A. Transverse waves characterized by the displacement of air molecules.
B. Longitudinal waves characterized by the displacement of air molecules.
C. Longitudinal waves characterized by pressure differences.
D. Both (B) and (C).
E. (A), (B), and (C).
5. In which of the following is the wavelength of the lowest vibration mode the same as the length of
the string or tube?
A. A string. D. An open tube.
B. A tube closed at one end. E. None of the above.
C. All of the above.
6. When a sound wave passes from air into water, what properties of the wave will change?
A. Frequency. D. Wavelength.
B. Wave speed. E. Both frequency and wavelength.
36
C. Both wave speed and wavelength.
1.5.2 Structured questions
7. Does the phenomenon of wave interference apply only to sinusoidal waves? Explain.
8. As oppositely moving pulses of the same shape (one upward, one downward) on a string pass
through each other, there is one instant at which the string shows no displacement from the
equilibrium position at any point. Has the energy carried by the pulses disappeared at this instant of
time? If not, where is it?
9. Can two pulses traveling in opposite directions on the same string reflect from each other?
Explain.
10. When two waves interfere, can the amplitude of the resultant wave be greater than the amplitude
of any of the two original waves? Under which conditions?
11. When two waves interfere constructively or destructively, is there any gain or loss in energy?
Explain.
12. Explain why your voice seems to sound better than usual when you sing in the shower.
13. An airplane mechanic notices that the sound from a twin-engine aircraft rapidly varies in
loudness when both engines are running. What could be causing this variation from loud to soft?
14. Explain how a musical instrument such as a piano may be tuned by using the phenomenon of
beats.
15. Fill in the gap
A. As a sound wave or water ripple travels out from its source, its -------------- decreases.
B. The vibrating air in a/an ----------------------------- has displacement antinodes at both ends.
C. For a /an ……………., the fundamental corresponds to a wavelength four times the length of the
tube.
D. The ……………….. refers to the change in pitch of a sound due to the motion either of the source
or of the observer. If source and observer are approaching each other, the perceived pitch is …….. If
they are moving apart, the perceived pitch is …………….
16. A bat, moving at 5.00 m/s, is chasing a flying insect. If the bat emits a 40.0 kHz chirp and
receives back an echo at 40.4 kHz, at what speed is the insect moving toward or away from the bat?
(Take the speed of sound in air to be v = 340 m/s.)
17. If you hear the horn of the car whose frequency is 216 Hz at a frequency of 225 Hz, what is their
velocity? Is it away from you or toward you? The speed of sound is 343 m/s
18. You run at 12.5 m/s toward a stationary speaker that is emitting a frequency of 518 Hz. What
frequency do you hear? The speed of sound is 343 m/s
37
19. If you are moving and you hear the frequency of the speaker at 557 Hz, what is your velocity? Is
it away from or toward the speaker? The speed of sound is 343 m/s
1.5.3 Essay type question
20. Read the following text and answer the question
Researchers have known for decades that whales sing complicated songs. Their songs can last for
30 min and a whale may repeat the song for two or more hours. Songs can be heard at a distances of
hundreds of kilometers. There is evidence that whales use variations in the songs to tell other whales
about the location of food and predators. Only the male whales sing, which has led some researchers
to think that songs are also used to attract a male.
The whale songs may be threatened by noise pollution. in the past 50 years, ocean noise has
increased due to human activities. Goods are transported across the ocean in larger ships than ever
before. Large ships use bigger engines. They produce low-frequency noise by stirring up air bubbles
with their propellers. Unfortunately, whales also use low-frequency sound in their songs, perhaps
because these sounds carry further than high-frequency sounds in the ocean. Propeller noise from
large ships is loud enough to interfere with whale songs at a distance of 20 km.
Question: Are regulations needed to protect whales from noise?
In your own words, describe the major issue that needs to be resolved about ocean noise pollution.
List three arguments for those who think regulations should require large ships to reduce noise
pollution. List three arguments for those who think regulations are not necessary.
38
UNIT 2: CLIMATE CHANGE AND GREENHOUSE EFFECT
Key unit Competence
By the end of the unit, I should be able to evaluate climate change and greenhouse effect.
My goals
Explain concepts of climate change
Explain causes of climate change
State the Stefan-Boltzmann law and apply it to emission rates from different surfaces
Outline the nature of black body radiation and its emissivity
Evaluate concept of emissivity and relate to emission rates for different surfaces.
Carry out an investigation on greenhouse effect
Make observations and ask questions on climate change, Identify problems and formulate
hypotheses to investigate climate change in surrounding environment
39
INTRODUCTORY ACTIVITY
Most of the solar radiation that is incident onto the Earth is absorbed and the rest is reflected back
into the atmosphere. Our Earth acts almost as a black body, thereby it radiates back to the space part
of the energy it has absorbed from the sun. The earth and its atmosphere is a part of the solar system. Life
on the Earth cannot exist without the energy from the sun.
a) Basing on Physics concepts, how do humans and plants get energy from the sun? Give the major
source of this energy?
b) Do humans and plants maintain the energy absorbed forever? Explain your reasoning using
physics concepts.
c) State and explain the scientific term used to describe a body that can absorb or emit radiations
that fall on them.
d) Basing on your ideas in (c) above what could be the effect on that body if:
i) It maintains the energy for a long time
ii) Reflects energy after a given time.
iii) Do you think that these reflected and absorbed radiations have effect on the Climate? Why?
Discuss your answers with your friends and even present it to your Physics teacher
2.1 SCIENTIFIC PROCESS BEHIND CLIMATE CHANGE
2.1.1 Black body radiation
Activity 2.1: black body radiation
- Try to get two clothes of the same kind (similar material) but of different colour black and White
- Soak them in water at the same time
- Display them to places of the same sunlight intensity.
- Check them after like 20 min, 30 min, or 40 min.
- Observe how they are drying up.
- Make a comprehensive report about your findings.
- Relate your findings to the concept of black body and hence define ‘a black body’
- From your deductions, explain what happens when the temperature of a black body increase
- You can share your observations and findings with your friends and even to your teacher.
An object that absorbs all radiation falling on it and therefore emitting radiation in whole spectrum
of wavelengths is called a blackbody. At equilibrium temperature a black body has a characteristic
frequency spectrum that depends only on its temperature.
A perfect blackbody is one that absorbs all incoming light and does not reflect any. At room
temperature, such an object would appear to be perfectly black (hence the term blackbody).
However, if heated to a high temperature, a blackbody will begin to glow with thermal radiation.
2.1.2 Laws of black body radiation
a) Stefan-Boltzmann law
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The law states that, “the power per unit area radiated by a surface of a black body is directly
proportional to the forth power of its temperature”.
4ATeP , (2.01)
where
- P is Power radiated in watts
- e is emissivity
- A is surface area in 2m
- 429 ..1067.5 KmW is Stefan-Boltzmann constant
- T is temperature in Kelvin
Using this formula, we can calculate the amount of power radiated by an object. A black body which
emit in whole spectrum of wavelength would have an emissivity of 1.
Since the earth is not a perfect black body, it has a certain emissivity value.
The emissivity is defined as the power radiated by a surface divided by the power radiated from a
perfect black body of the same surface area and temperature.
In simpler terms, it is the relative ability of a surface to emit energy by radiation. A true
blackbody would have an emissivity of 1 while highly polished silver could have an emissivity of
around 0.02. The emissivity is a dimensionless quantity.
b) Wien’s displacement law
It states that “the maximum wavelength of the emitted energy from a blackbody is inversely
proportional to its absolute temperature”.
This law was formulated by the German physicist Wilhelm Wien in 1893 who related the
temperature of a black body and its wavelength of maximum emission following the equation
bT max, (2.02)
where b is Wien's constant approximately equal to 2.9 × 10−3 m K, T is the absolute temperature in Kelvin and
max wavelength of maximum emission
It is thus found out that as the temperature of blackbody increases, the total amount of light emitted
per second increases, and the wavelength of the spectrum's peak shifts to bluer colors.
Quick check 2. 1: When an iron bar is heated at high temperatures it becomes orange-red and its
color progressively shifts toward blue and white as it is heated further. Explain this observation?
Remember: It is not good to put on black clothes on a sunny day. This is because these dark clothes
will absorb more radiations from the sun which may be harmful to our health
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2.1.3 Black body radiation curves
Fig.2. 1 Black body radiation curves showing peak wavelengths at various temperatures
This Fig.2.1 shows how the black body radiation curves change at various temperatures.
The graph indicates that as the temperature increases, the peak wavelength emitted by the black body
decreases. It therefore begins to move from the infra-red towards the visible part of the spectrum.
Again, none of the graphs touch the x-axis so they emit at every wavelength. This means that some
visible radiation is emitted even at these lower temperatures and at any temperature above absolute
zero, a black body will emit some visible light.
Features/Characteristics of the Graph
As temperature increases, the total energy emitted increases, because the total area under the
curve increases.
It also shows that the relationship is not linear as the area does not increase in even steps. The rate
of increase of area and therefore energy increases as temperature increases.
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2.1.4 Checking my progress
For the questions listed below, re-write the questions in your notebooks and CIRCLE the best
alternative
1. What is the black body or an ideal radiator?
A. the body which transmits all the radiations incident upon it
B. the body which absorbs all the radiations incident upon it
C. the body which reflects all the radiations incident upon it
D. none of the above
2. As a radiator, the black body emits the maximum possible thermal radiation
A. at the constant single wavelength C. at all Possible wavelengths
B. at a maximum wavelength D. none of the above
3. Which of the following sentences are correct for black body
(i) The black body is a hypothetical body
(ii) The black body is a real body
(iii) The black body is used as a standard of perfection against which the radiation characteristics of
other bodies are compared
A. sentences (i) and (ii) C. sentences (ii) and (iii)
B. sentences (i) and (iii) D. all the sentences (i), (ii) and (iii)
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2.2 INTENSITY OF THE SUN’S RADIATION REACHING PLANETS
2.2.1 Intensity of the sun’s radiation and albedo
Activity 2.2: Intensity of the sun’s radiation
Below is a stove of a gas cooker producing heat (You can use a Bunsen burner in your laboratory)
Fig.2. 2 Stove of a gas cooker
Questions:
A. Light up the stove or Bunsen burner provided
B. Come close to the lighting Bunsen or stove. In your words write down what you are experiencing
in terms of heat.
C. Place conductor (You can use an old iron sheet) between you and the source. Can you still
receive the same amount of heat from the source? Explain why?
D. Relating the scenario above with the transfer of heat (radiation) from the sun, how does sun’s
heat (radiations) reaches us, and other planets,
E. If you are far away from the source, can you receive the same amount as someone near it? Relate
it to the transfer of heat from the sun to different planets explain your reasoning.
F. In your own words, explain the factors that determine a body’s ability to absorb or reflect a
certain radiation
Sun produces heat of very high intensity that is spread and then received by all surrounding objects.
These objects include all the planets and other objects around it.
The intensity of the sun (at the top of the earth’s atmosphere) is approximately 1400 W/m2 also
known as the solar constant. The amount received on the earth surface is slightly below 1400 w/m2.
The main reasons for variation in intensity include:
The shape of the earth: The earth has a spherical shape and therefore the sunlight is more spread
out near the poles because it is hitting the earth at an angle, as opposed to hitting the earth
straight-on at the equator. There are also fewer atmospheres at the equator, allowing more
sunlight to reach the earth. Therefore, the intensity varies depending on the geographical
latitude of the earth’s location.
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The earth's rotation: all areas are not consistently exposed to sunlight. Areas that are
experiencing 'nighttime' are not receiving a lot of the sun's power; therefore the time of the day or
night will affect the solar constant.
The angle of the surface to the horizontal at that particular location: When the Sun is
directly overhead, its rays strike Earth perpendicular to the ground and so deliver the maximum
amount of energy. When the Sun is lower in the sky, a sunbeam strikes the ground at an angle
and so its energy is "spread out" over a larger area
The solar constant represents the mean amount of incoming solar electromagnetic radiation per
unit area on the earth's surface. This constant takes into account all types of solar radiation,
including UV and infrared. The accuracy of the solar constant is questionable due to the
following generalizations: This radiation is assumed to be incident on a plane perpendicular to
the earth's surface. It is assumed that the earth is at its mean distance from the sun.
Our seasons also determine how much Sun’s radiation strikes a square meter of ground in a given
place on the planet's surface at a given time of the year. The sun’s radiation is maximum in the
summer and it is minimum in winter.
Scientists use a quantity called "albedo" to describe the degree to which a surface reflects light that
strikes it. It can be calculated by the ratio of reflected radiation from the surface to the incident
radiation upon it.
powerincidenttotal
powerscatteredtotalalbedo
. (2.03)
The albedo has no units since it is a ratio of the similar quantities.
Being a dimensionless fraction, it can also be expressed as a percentage and is measured on a scale
from 0 (0%) for no reflective power to 1 (100%) for perfect reflectors. The earth's albedo is about
0.3, meaning, on average, 30% of the radiation incident on the earth is directly reflected or scattered
back into space. An object that has no reflective power and completely absorbs radiation is also
known as a black body
Fig.2. 3: The transmission of light (heat) from the sun to the Earth
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The table below gives you some values of estimated albedo for various surfaces expressed as
percentages:
Surface Albedo (%) Surface Albedo% Surface Albedo (%)
Fresh snow
or ice 60-90
Tropical
forests 13 Fresh snow 80-95
Old, melting
snow 40-70 Woodland 14
Water
bodies 10-60
Clouds 40-90 Sandy
desert 37 Grass 25-30
Desert sand 30-50 Sea ice 25-60 Crops,
grasslands 10-25
Soil 5-30 Grassland 20 Forests 10-20
Tundra 15-35 Snowy
vegetation 20-80 Light roof 35-50
Grasslands 18-25 Stony
desert 24 Dark roof 8-18
Forest Snowy Ice 80 Brick, stone 20-40
Water Water 8-10 Concrete,
dry 17-27
Table 2. 1 Albedo for various surfaces
Some other facts about sun
1. At its centre, the sun reaches temperature of 15 million degrees Celsius
2. The sun is all the colors mixed together, this makes it appear white to our eyes.
3. The sun is mostly composed of hydrogen (70%) and Helium (28%)
4. The sun belongs to the main Sequence G2V star (Yellow Dwarf)
5. The sun is about 4.6 billion years old
6. The sun is about 100 times wider than the earth and 3330 000 times as massive
Activity 2.3:
1. a. With clear explanations, explain the approximate spectral composition of the Sun's radiation
before it interacts with Earth's atmosphere?
b. Is the amount of solar energy that reaches the top of Earth's atmosphere constant? Explain giving
valid examples and evidence.
c. Are all wavelengths of Sun’s radiation transmitted equally through Earth's atmosphere? Explain
your reasoning.
2. a. What effect does absorption have on the amount of solar radiation that reaches Earth's surface?
b. List down other processes (besides absorption) that affect radiation reaching the earth’s surface?
c. What can be percentage of incoming solar radiation that is affected by absorption and scattering
(or reflection)?
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3.a. Jane Says that clouds have a high albedo while Pierre says land vegetation has a low albedo?
Using Scientific explanations, Discuss what they base on to make their deductions
b. What do you think are major factors that influence the insolation at a particular location on a
particular day? How do they affect it?
c. What latitudinal regions experience least variation in day-to-day solar radiation? Which one
experiences the greatest? Why?
2.2.2 Factors affecting Earth’s albedo
Activity.2.4
The text below is incomplete as it misses some of the technical terms. Using the knowledge and idea
about albedo, re-write the text in your notebook and fill the spaces with the words given in the
brackets (Aerosols, Deforestation, Lifetime, Climate, Infrared Radiation) to complete the text.
A. There are many factors that affect the Earth's _________. Snow and ice are highly reflective so
when they melt, _____________ drops.
B. Forests have a lower ________ than open land so ___________ increases ___________
C. __________ have a direct and indirect effect on _______________.
D. The direct effect is by reflecting sunlight back into space, cooling the Earth.
E. The indirect effect is when aerosol particles act as a cloud condensation nucleus, affecting the
formation and ______________of clouds.
F. Clouds in turn influence global temperatures in various ways.
G. They cool the ________ by reflecting incoming sunlight but can also warm the ___________ by
trapping outgoing _____________from the surface
Among other factors, the following are some of the factors that affect the albedo of the earth:
Clouds. The atmosphere is usually covered with clouds that usually pass over the earth’s surface.
This leads to reduction or increase in the temperature of the earth’s surface. This is because these
clouds may absorb or reflects back sun’s light to the free space. However, this depends on the
distance from which the clouds are from earth’s surface. When sun’s radiation is reflected, the
earth’s surface is cooled and when it is absorbed the earth is warmed.
Oceans While observing from the space, you will find out that water bodies appear differently
from land surfaces. They appear darker and therefore absorb more sun’s radiations than land.
However, some of the radiations heating the water surface (ocean) may be carried away by the
currents while others may form water vapor.
Thick vegetation covers or forested areas. Places covered with vegetation absorb a lot of sun’s
radiation. This is because the vegetation cover provides a dark surface which absorbs more
radiations than the bare land.
Surface albedo. Different surfaces appear differently. Light coloured surfaces absorb different
amounts of radiations than dark coloured surfaces. Snow covered areas are highly reflective.
They thus absorb less amounts of energy (Sun’s radiation). The snow cover reduces the heating
effect of the earth’s surface. However, if temperatures reduce, the snow cover reduces leading to
the absorption of radiation by the exposed ground surface.
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2.2.3 Checking my progress
For questions 1-4 below, re-write them in your notebook and CIRCLE the best alternative of your
choice
1. Which of the following has high Albedo?
A. asphalt parking lot C. they have the same albedo
B. snow-covered field D. Some information is missing for this question
2. Imagine you are having two places: a desert and a forest. Which one has lower albedo,?
A. desert C. they have the same albedo
B. forest D. This question lacks some information
3. Imagine you are looking at two Areas of land while flying over in a jet at midday. Plot #A looks
very bright. Plot #B looks very dark. Which area of land has a lower albedo?
A. Plot #A
B. Plot #B
C. they have the same values for albedo
D. more information is needed to answer this question
4. Refer to the list of albedo values (below). Order these three surfaces - fresh snow, grasslands, and
asphalt - from highest albedo to lowest albedo.
A. snow, asphalt, grasslands D. asphalt, snow, grasslands
B. asphalt, grasslands, snow E. grasslands, snow, asphalt
C. snow, grasslands, asphalt F. grasslands, asphalt, snow
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2.3 GREENHOUSE EFFECTS
Fig.2. 4: Greenhouse effect
Discovery Activity 2.5
a) What do you know about greenhouse?
b) Different activities like industrialization and others give out gases after burning fossil fuels.
(i) What special name is given to these gases?
(ii) If these gases accumulate in the atmosphere, what effect do they have on to the temperature of
the earth and its atmosphere?
c) Suggest measures that can be done to limit high accumulation of these gases in the atmosphere.
d) Discuss your findings with your classmates and even to your teacher. Come up with a general
stand from your findings
The relationships between the atmospheric concentration of greenhouse gases and their radiative
effects are well quantified. The greenhouse effect has the root from greenhouses that becomes
warmer when heated by sun’s radiation. The mode of operation of a green house is that a part of the
sunlight radiations incident on the ground surface of the greenhouse are absorbed and warms the
surface inside the greenhouse. Both the reflected radiations and the heat emitted by the ground
surface in the greenhouse are trapped and re-absorbed inside the structure. Thus, the temperature
rises inside the greenhouse compared to its surrounding environment.
Therefore, the greenhouse effect heats up the earth’s surface because the green gases that are in the
atmosphere prevent radiations from leaving the atmosphere. The absorption of these radiations
contributes to the increase of the atmosphere’s temperature.
Note: green gases act as a glass or plastic in greenhouses
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A greenhouse is constructed by using any material that allows sunlight to pass through usually plastic
or glass. This prevents reflected radiations from leaving the structure thereby leading to the increase
in the temperature within. If a small puncture is made on to the greenhouse, the temperature within
reduces.
PROJECT: 2.1 Construct a greenhouse (Can be done in a period of 3 months)
In this project you may need
Polyethene paper or plastic or glass.
Wood
Nails
Any fiber that can be used while Tying
Procedures
a) Using materials listed above, construct a small greenhouse. It Can be done at School or at home.
b) Sow any seed inside.
c) After seeds have germinated, see the changes in the development of the plant.
d) Make a comprehensive Report about your Greenhouse. Include temperature and vapor changes
within the green house.
e) Share it with your friends or your teacher.
By definition therefore, Greenhouse effect is the process by which thermal radiation from the sun is
prevented from leaving the atmosphere and then re-radiated in different directions.
Since some of these re-radiated radiations come back to the earth’s surface, they lead to the increase in
the temperature of the earth’s surface leading to global warming.
Fig.2. 5: (a) Greenhouses in one of the parts of Rwanda and (b) emission of greenhouse gases.
2.3.1 Greenhouse gases
Some gases in the earth's atmosphere act a bit like the glass in a greenhouse, trapping the sun's heat
and stopping it from leaking back into space.
Many of these gases occur naturally, but human activity is increasing the concentrations of some of
them in the atmosphere, in particular:
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carbon dioxide (CO2)
methane
nitrous oxide
fluorinated gases
CO2 is the greenhouse gas most commonly produced by human activities and it is mainly
responsible for man-made global warming. Its concentration in the atmosphere keeps on
increasing with industrialization.
Other greenhouse gases are emitted in smaller quantities, but they trap heat far more effectively than
CO2, and in some cases are thousands of times stronger. Methane is responsible for 17% of man-
made global warming, nitrous oxide for 6%.
Causes for rising emissions:
Burning coal, oil and gas that produce carbon dioxide and nitrous oxide.
Cutting down forests (deforestation). Trees help to regulate the climate by absorbing CO2 from the
atmosphere. So when they are cut down, that beneficial effect is lost and the carbon stored in the
trees is released into the atmosphere, adding to the greenhouse effect.
Increasing livestock farming. Cows and sheep produce large amounts of methane when they digest
their food.
Fertilizers containing nitrogen produce nitrous oxide emissions.
Fluorinated gases produce a very strong warming effect, up to 23 000 times greater than CO2.
Thankfully these are released in smaller quantities and are being phased down by European Union
regulation.
Activity 2.6: Emitted greenhouse gases worldwide from 1990 to 2005
Below is a bar graph showing emitted Greenhouse gases worldwide from 1990 to 2005. Use it to
answer the questions that follow.
Fig.2. 6 Emissions of greenhouse gases worldwide from 1990 to 2005 by Rwanda Environment Management
authority (REMA)
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a) From your analysis (using the graph) which kind of gas was emitted in excess for the specified
period? What could be the factors that led that gas to be emitted in large quantities?
b) What do you think one can do to limit such emissions?
c) From your own point of view, do you think it’s a good idea to stop completely emission of these
gases? Explain your reasoning by giving valid examples.
Solutions to reduce the impact of greenhouse gases
High efficiency during power production
replacing coal and oil with natural gas
combined heating and power systems (CHP)
renewable energy sources and nuclear power
carbon dioxide capture and storage
Use of hybrid vehicles.
2.3.2 Impact of greenhouse effect on climate change.
With the greenhouse effect, the earth is unable to emit the excess heat to space and this leads to
increase in atmosphere’s temperature and global warming. Scientists have recorded about 0.75°C
increase in the planet's overall temperature during the course of the last 100 years. The increased
greenhouse effect leads to other effects on our climate and has already caused: (REMA)
Greater strength of extreme weather events like: heat waves, tropical cyclones, floods, and other
major storms.
Increasing number and size of forest fires.
Rising sea levels (predicted to be as high as about 5.8 cm at the end of the next century).
Melting of glaciers and polar ice.
Increasing acidity in the ocean, resulting in bleaching of coral reefs and damage to oceanic
wildlife.
2.3.3 Global warming
Global warming is the persistent increase in temperature of the earth's surface (both land and water)
as well as its atmosphere. Scientists have found out that the average temperature in the world has
risen by about 0.750C in the last 100 years and about 75% of this rise is from 1975.
Previously the changes were due to natural factors but currently the changes are due to both natural
and human activities. From research, natural greenhouse maintains the temperature of the earth
making it a better place for human kind and animal life. However ever since the evolution of
industries, there has been significant change in the temperature. The causes are both natural and
human activities:
a-Human activities
Burning of fossil fuels: These emit carbon dioxide gases when heated that accumulate in the
atmosphere. These gases absorb and may not allow sun’s radiation to pass through. This in turn
leads to an increase in the temperature of the earth’s atmosphere, hence global warming. These
fuels are burnt in vehicles and in industries.
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Deforestation. Plants use carbon dioxide in manufacturing their food. This implies that trees
reduce amount of carbon dioxide in the atmosphere. Cutting down these trees therefore leads to
part of carbon dioxide remains unused. This is a big problem
Agriculture: Agriculture is a good practice. Though if not handled with care, it may lead to
destruction of nature which is a big problem
And all other infrastructure development: These include, urbanization, road construction and
places for settlement. These have contributed to the destruction of nature.
b- Natural causes
Volcanicity: When volcanoes erupt, they throw out large volumes of sulphur dioxide (SO2),
water vapor, dust, and ash into the atmosphere. Although the volcanic activity may last only a
few days, the large volumes of gases and ash can influence climatic patterns for years. Millions
of tones of sulphur dioxide gas can reach the upper levels of the atmosphere (called the
stratosphere) from a major eruption.
Ocean currents: Oceans plays a major role in the change of climate. Oceans cover about 71% of
the Earth and absorb about twice as much of the sun's radiation as the atmosphere or the land
surface. Ocean currents move vast amounts of heat across the planet - roughly the same amount
as the atmosphere does. But the oceans are surrounded by land masses, so heat transport through
the water is through channels.
All the above practices lead to high concentration of greenhouse gases in the atmosphere especially
carbon dioxide gases.
Note: If these greenhouse gases were completely not there, the Earth would be too cold for humans,
plants and other creatures to live.
Can you now see the importance of these greenhouse gases! Though they cause greenhouse effect,
they are responsible for regulating the temperature of the earth.
Global warming is damaging the earth's climate as well as the physical environment. One of the most
visible effects of global warming can be seen in the Arctic region where glaciers, permafrost and sea
ice are melting rapidly. Global warming is harming the environment in several ways. Global
warming has led to: desertification, increased melting of snow and ice, sea level rise, stronger
hurricanes and cyclones
2.3.4 Checking my progress
1. What do you understand by the term "greenhouse" effect?
2. With clear explanations, explain why it is called the "greenhouse" effect?
3. From your own reasoning and understanding, why do you think Environmental experts have
become worried about the greenhouse effect?
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2.4 CLIMATE CHANGE
Activity 2.7
Having discussed the intensity of Sun’s radiation reaching the earth and the black body radiation
theory, discuss the following questions:
What are the effects of these radiations on the earth and its atmosphere after absorption and
reflection?
From your own understanding, what would happen if there is imbalance between the absorbed
and radiated energy in the earth’s atmosphere.
Can that incidence be avoided? How? Write in your own words all the scientific measures that
can be done to avoid that kind of situation.
Activity 2.8:
Fig.2. 7:
From the picture above,
1. What do you observe from the picture above?
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2. What could be the major causes of such situation in most of the communities especially in
Rwanda?
3. How does this situation affect the welfare of the people in a given community?
4. In your view, suggest the preventive practices people should do to avoid such situations?
2.4.1 Climate change and related facts
There has been variation in the atmospheric conditions in a given time. This has affected the seasons
leading to a less output of our produce especially from agriculture, fishing and other activities.
These changes are sometimes for a short time but also may take a long time. Some of these changes
result from our practices like farming, industrialization, urbanization, mining and other infrastructure
developments. Care should be taken so as these changes in the atmospheric conditions can be
avoided.
Activity 2.9
1. From your experience, have you ever experienced changes in atmospheric conditions? How long
did it take?
2. In your own views discuss the causes of those changes. Are these changes harmful or useful?
Explain your reasoning
3. As a member of the community discuss how you identify that there is climatic change
4. If an investor wants to start an agricultural farm in your community. Depending on related reality
of climatic conditions of your area, what advices and information would you give to that
investor?
Climate is usually defined as the "average weather," or more rigorously, as the statistical
description in terms of the mean and variability of relevant quantities over a period of time ranging from months to thousands of years. The classical period is 3 decades, as defined by the
World Meteorological Organization (WMO).These quantities are most often surface variables such
as temperature, precipitation, and wind. Weather is measured in terms of the following parameters:
wind, temperature, humidity, atmospheric pressure, cloudiness, and precipitation. In most places,
weather can change from hour-to-hour, day-to-day, and season-to-season. Climate can be described
as the sum of weather. While the weather is quite variable, the trend over a longer period, the
climate, is more stable.
However climate change can be observed over a longer period of time. Climate change refers to any
significant change in the climate parameters such as temperature, precipitation, or wind patterns,
among others, that occur over several decades or longer Natural and human systems have adapted to
the prevailing amount of sunshine, wind, and rain. While these systems can adapt to small changes in
climate, adaptation is more difficult or even impossible if the change in climate is too rapid or too
large. This is the driving concern over anthropogenic, or human induced, climate change. If climate
changes are too rapid then many natural systems will not be able to adapt and will be damaged and
societies will need to incur the costs of adapting to a changed climate (REMA)
Some of important terms we need to know
• Climate feedback: This refers to a process that acts to amplify or reduce direct warming or
cooling effects.
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• Climate lag: This is the delay that can occur in a change of some asp ect of climate due to the
influence of a factor that is slow acting.
• Climate model: This is a quantitative way of representing the interactions of the atmosphere,
oceans, land surface, and ice. Models can range from relatively simple to quite comprehensive
This explains a delay that occurs in climate change as a result of some factors that changes only
very slowly. For example, the effects of releasing more carbon dioxide into the atmosphere occur
gradually over time because the ocean takes a long time to warm up in response to these
emissions.
PROJECT WORK 2.2:
1. Using a case study of Rwanda, by identifying different areas or provinces, Design a good chat that
may be in tabular form showing differences in the amounts of sunshine, rainfall, humidity and
precipitation in those areas or provinces.
2. Still using your findings, what has led to the difference in the climate changes in these areas yet
they are all found in Rwanda?
3. Compare and contrast the climate of these provinces
4. Make a compressive report. You can share it with your friends and finally to the teacher.
2.4.2 Causes of climate change.
Activity.2.10
Read the text below and answer the questions that follow.
In Rwanda, like in many other developing countries, large efforts are being invested in reducing
vulnerability to climate change by taking actions needed to increase preparedness for climate change,
including specific interventions (such as larger storm drains or new crop varieties) and also broader
social economic strategies (such as relocating households from high risk zones). This is called
adaptation to climate change.
The terminology of “Climate resilience” is usually used to describe a broader agenda than
adaptation as described above. It captures activities which build the ability to deal with climate
variability – both today and in the future. Among other causes, the concentration of green gases in
the atmosphere greatly affects the temperature of the Earth
Questions
1. Explain the meaning of the underlined terms in the text
2. From the text above, what is the major cause of climate change
3. Discuss some of the strategies that the Rwandan Government is doing to fight the problem of the
climate change. State some of the actions taken as described in the text
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4. The writer in the text talked about industrialisation as a practice that can lead to climate change.
From your understanding and experience, how is this possible?
Physics behind climate change and causes
The climate of the earth is controlled by its absorption and the subsequent emission of that energy.
The Earth’s surface temperature is determined by the balance between the absorption and emission
of Sun’s radiation.
The major cause of climate change is the concentration of greenhouse gases, especially water vapor
and carbon dioxide. These gases trap thermal radiation from the earth’s surface and this effect keeps
the surface warmer than it would be.
Human activities are major factors that lead to natural greenhouse effect. Most of activities done by
human lead to high concentration of greenhouse gases. From research it has been found that the
concentration of carbon dioxide has risen by about 30% in this era as compared to pre-industrial era.
This gives a projection that the concentration of these greenhouse gases is still increasing day and
night as people continue using fossil fuels.
Such activities include bush burning, burning of fossil fuels, deforestation and agriculture. All these
activities have a strong impact on the climate of a given area as they may lead to either warming or
cooling the land.
On another hand, industries have also led to the change in climatic conditions as they emit carbon
gases into the atmosphere. From what is happening currently, the climatic conditions are worsening
if the world becomes more industrialized.
Man is trying to limit this by making machines that emit less carbon gases (REMA)
Fig.2. 8 An operating industry giving out gases. These gases affect the atmosphere that leads to climate change.
NOTE: It is very important to have to work and do different activities that may lead us to develop
and our country too. But care should be taken NOT to destroy the Nature.
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Activity 2.11
1. What do you think are the factors that lead climatic change in your area? Make a general
conclusion using a case study of Rwanda.
2. The earth's climate can be affected by natural factors that are external to the climate system, such
as changes in volcanic activity, solar output, and the earth's orbit around the sun.
How can people limit these factors to have a better climate? Share with your friends and even the
teacher.
2.4.3 Checking my progress
1. What do you understand by the following terms as used in this concept?
A. Weather D. Humidity
B. Climate E. Temperature
C. Climatic change
2. Using Physics Concepts, discuss why different areas found in the same region may have different
climatic conditions.
3. What are some of the strategies as a Rwandan have you set to fight these changes?
4. Plan and write an essay about climatic changes in Rwanda.
5. Study the graph given below and answer the questions that follow
Fig.2. 9 Variation of the annual average temperature in 0C (1971-2009) at Kigali station Airport and Kamembe
Airport Station (Source: Data analysis provided by the Rwanda meteorological service) (REMA)
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(a) From the graph, which station had higher temperature? Explain why the selected station show
high values of temperature relating to the factors that affect climate.
(b) What was the recorded temperature of the two stations in 2005?
(c) Discuss with relevant examples why there is a need to record temperatures of a given place after a
given time.
6. Let’s have our minds rest using physics
Below is a crossword puzzle about climatic change. Check the left of the puzzle and find the
corresponding word in the puzzle
This is really interesting!!!!!!!
What you can do to save your/our climate
Learn about climate change share knowledge and information on climate change. By sharing
knowledge and strategies to combat climate change with others you will increase awareness on
climate change issues. Talk with your colleagues and leadership about how you can better
integrate climate change considerations;
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Learn about how climate change impacts your sector. By looking into the negative impacts of
climate change on your business processes and coming up with adaptation solutions you will
make it climate-proof and reduce your sector’s vulnerability to climate change
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2.5 CLIMATE CHANGE MITIGATION
2.5.1 Climate change mitigation
Activity 2.13
READ AND CONTRIBUTE
The government of Rwanda is trying to sensitize people not to cut down trees for charcoal, Drying
wetlands for farming activities and regulating people from approaching wetlands, forests (Both
Natural and artificial) and Fighting all activities that may lead to climate change.
a) As a good citizen of Rwanda, Do you support these plans of the government? Support your stand
with clear justifications
b) If Yes what have you done to implement some of these policies?
c) What are some of the New Technologies that the government is advocating for to stop these
negative climate changes?
Climate change mitigation refers to efforts to reduce or prevent emission of greenhouse gases.
Mitigation can mean using new technologies and renewable energies, making older equipment more
energy efficient, or changing management practices or consumer behavior (IPCC, 1996).
Climate change is one of the most complex issues we are facing today. It involves many dimensions
science, economics, society, and moral and ethical questions and is a global problem, felt on local
scales that will be around for decades and centuries to come. Carbon dioxide, the heat-trapping
greenhouse gas that has driven recent global warming, lingers in the atmosphere for centuries, and
the earth (especially the oceans) takes a while to respond to warming.
So even if we stopped emitting all greenhouse gases today, global warming and climate change will
continue to affect future generations. In this way, humanity is “committed” to some level of climate
change.
Because we are already committed to some level of climate change, responding to climate change
involves a two-pronged approach:
1. Reducing emissions and stabilizing the levels of heat-trapping greenhouse gases in the
atmosphere (“mitigation”);
2. Adapting to the climate change already in the pipeline (“adaptation”).
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2.5.2 Mitigation and adaptation
Fig.2. 10: Solar panels have been used to reduce some of the problems caused by other sources of energy
Because of these changes in climatic conditions, man has devised all possible measures to see how
he can live in harmony on this planet. This has made man to think harder so that these green gases
can be minimized.
The process of preventing all these greenhouse gases is what is known as mitigation. This is very
important as it is aimed at controlling the rise in temperatures of the earth while regulating earth’s
temperature.
The main goal of mitigation is to reduce human interference to nature thereby stabilizing the
greenhouse gas levels in a given time to allow ecosystem to adapt naturally to the climate changes.
Care should be taken while these adjustments are made not to affect food production and other
economic developments.
Among other strategies, mitigation strategies include retrofitting buildings to make them more
energy efficient; adopting renewable energy sources like solar, wind and small hydro-electric plants
helping cities develop more sustainable transport such as bus rapid transit, electric vehicles and
bio fuels, promoting more sustainable uses of land and forests and creating carbon sinks like in
big oceans in case there are no alternatives.
PROJECT.2.3
GOAL: To construct your control greenhouse model and your enhanced greenhouse model, begin by
collecting all the materials other than the dry ice.
MATERIALS
• Coloured markers or pencils
• Distilled water
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• Two drinking water bottles (empty, plastic, same size, clear)
• Dry ice (broken pieces) Flame source—candle
• Graduated cylinder Lamps (radiant heat)
• Modelling clay Paper clip
• Plastic tubes Scissors (or razor)
• Stop watch or watch with second hand Two cups
• Thermometers Tongs (to handle dry ice)
Procedures:
1. Prepare the enhanced greenhouse model,
2. Use a flame from the candle to heat the end of a paper clip.
3. Use the hot paper clip to make a small hole in the side of one of the plastic drinking bottles.
4. Make this hole about half way between the top and bottom of the bottle.
5. Make sure that the plastic tubing will fit into the hole.
6. Put 200 ml of distilled water into each of the two bottles.
7. Place the plastic tubing into the hole that you made for the “enhanced greenhouse” effect model.
8. Use clay to prevent any air from leaking out once the experiment begins.
9. Place a thermometer into the top of each bottle so that the end of the thermometer is in the centre
of the bottle.
10. Hold in place and seal off the bottle top opening using the modelling clay.
11. Prepare the container for inserting the dry ice vapor, obtain two Styrofoam cups. One should be
larger than the other or you can cut one to fit beneath the other.
12. Punch a hole in the bottom of the larger cup on the top.
13. Insert the plastic tubing and use the clay to prevent any leakage of the carbon dioxide.
14. Obtain a piece of dry ice that fits into the smaller Styrofoam cup.
15. Add enough water to begin sublimation.
16. Connect the plastic tubing to the bottle and let the carbon dioxide gas to flow into the bottle for
90 seconds.
17. Take the tubing out and close the tubing hole with clay once you have added the carbon dioxide.
18. Place both bottles the same distance from a heat lamp and turn on the light
19. Begin recording the temperature as soon as you have closed the hole and turn on the light.
Record the temperature every two minutes for twenty minutes in the table.
20. Construct a graph of your data.
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2.5.3 Checking my progress
The graph below shows the emission of Carbon emissions from fossil fuels of a certain region in
Africa from 1990 to 2014. Study the graph carefully and answer the questions that follow
Fig.2. 11 Global carbon emission from fossil fuels, 1900-2010 (REMA)
1. By observing clearly the graph, explain the trend of the Curve from 1990 to 2010. With the
knowledge and ideas you have acquired from this Unit, Discuss factors that might have led to the
rise of the shape of the graph
2. Suppose the Curve was to be extended to 2018, do you think the curve would continue the trend
or would Fall? Explain your reasoning
3. Discuss some of the major causes of increased carbon emissions in our Society,
4. Come up with possible measures that can assist the community to have less carbon emissions.
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2.6 END UNIT ASSESSMENT
2.6.1 Multiple choice type questions.
Re-write the questions below in your notebook and CIRCLE the best alternative
1. The emissivity (ε) can be defined as the ratio of
A. emissive power of real body to the emissive power of black body
B. emissive power of black body to the emissive power of real body
C. reflectivity of real body to emissive power of black body
D. reflectivity of black body to emissive power of real body.
2. Imagine two planets. Planet A is completely covered by an ocean, and has and overall average
albedo of 20%. Planet B is blanketed by clouds, and has an overall average albedo of 70%. Which
planet reflects more sunlight back into space?
A. Planet A
B. Planet B
C. the two planets reflect the same amount of light
D. more information is needed to answer this question
3 _______________ is a term used to a process that acts to amplify or reduce direct warming or
cooling effects
A. Climate change C Climate feedback
B. Weather D Climate model
4 The filament of an electric bulb has length of 0.5 m and a diameter of 6x10-5 m. The power rating
of the lamp is 60 W Assuming the radiation from the filament is equivalent to 80% that of a perfect
black body radiator at the same temperature. The temperature of the filament is (Stefan Constant is
5.7x10-8 Wm-2K-4):
A. 1933 K C. 64433333.3 K
B. 796178.3 K D.60 K
5 The long-term storage of carbon dioxide at the surface of the earth is termed as
A. Black body radiation C. Solar radiation management
B. Thermal expansion D. Sequestration
6. The balance between the amount of energy entering and exiting the Earth system is known as
A. Radiative balance C. Paleoclimatology
B. Black body Radiation D. Solar radiation
7. The following are examples of green gases except
A. Carbon dioxide C Methane
B. Nitrous oxide D. Oxygen
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8. The government of Rwanda is advising the people to conserve the nature. This is intended to limit
the incidence of rise in the temperature. This conservation of nature
A. Reduces the amount of water vapor that leads to increase in temperature
B. Reduces the amount of Carbon dioxide in the space
C. Increases the amount of plant species that is required to boost our tourism industry
D. Provides a green environment for human settlement
2.6.2 Structured questions
1. a) State Wien’s displacement law and its practical implications
b) Use the graph indicated below to answer the questions that follow
i) What does the graph explain?
ii) Explain the spectrum that is found between temperatures of 4000 and 7000 K
iii) Why do you think the three curves have different shapes
2. Discuss any 4 main reasons that brings about variation of sun’s Intensity
3.a) Calculate the albedo of a surface that receives 15000 Wm-2 and reflects 15 KW.m-2
Comment on the surface of that body
b) Discuss some of the scientific factors that affect planets Albedo
4.a) What do you understand by the following terms?
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i) Climate change as applied in physics
ii) Greenhouse Effect
b) With Clear explanations, discuss how Greenhouse effect can be avoided
2.6.3 Essay type questions
1. Clemance a year 4 student in the faculty of engineering in University of Rwanda found out in her
research that a strong metal at 1000k is red hot while at 2000k its white hot. Using the idea of black
body, explain this observation.
2. John defined black body as anybody that is black. Do you agree with his definition? If YES why?
and if NOT why not? Also sketch curves to show the distribution of energy with wavelength in the
radiation from a black body varies with temperature.
3. An electric bulb of length 0.6 m and diameter 5 x 10-5 m is connected to a power source of 50 W.
Assuming that the radiation from the bulb is 70% that of a perfect black body radiator at the same
temperature, Estimate the steady temperature of the bulb. (Stefan’s constant = 5.7 x 10 - 8 W m 2 K-4.)
4. Write short notes about greenhouse effect and explain all its effects.
5. What do you understand by the term green gases? How do these gases contribute to the global
warming?
6. REMA is always advising people to plant more trees and stop cutting the existing ones. Using
scientific examples, explain how this is aimed at controlling global warming
7. Explain climate change mitigation and explain why it’s important.
8. Explain what happens to most radiation that is absorbed by the surface of earth?
9. Is there difference between sensible and latent heat?
10. Write short notes on the following terms as applied in climate change
i) Climate feedback
ii) Climate lag
iii) Climate model
11. Plan and write a good composition about causes of climate change and how it can be controlled.
(Your essay should bear introduction, body and conclusion,)
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UNIT 3: APPLICATION OF PHYSICS IN AGRICULTURE
Fig.3. 1: A farmer spraying rice
Key unit Competence
By the end of the unit the learner should be able to evaluate applications of Physics in Agriculture.
My goals
Describe the atmosphere and its constituents.
Outline variation of atmospheric pressure, air density and water vapour with altitude.
Evaluate how heat and mass transfers occur in the atmosphere.
Apply knowledge of physics to illustrate changes in water vapour atmospheric pressure, and air
with altitude.
Evaluate and interpret physical properties of soil (soil Texture and structure).
Evaluate why air, temperature and rainfall limit economical activities in Agriculture.
Explaining how mechanical weathering and soil erosion impact economic activities in
agriculture.
Explaining clearly how agrophysics plays an important role in the limitation of hazards to
agricultural objects and environment in our country.
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Introductory activity: Role of machines in agriculture
It is very important to know the role of Physics in agriculture and environment. Knowledge in
physics can contribute more in the limitation of hazards in agriculture (soils, plants, agricultural
products and foods) and the environment based on suitable programs of transformation and
modernization of agriculture in our country.
Look at the image given in Fig.3.1 above!
a. What do you observe? Is there any application of prior knowledge of Physics learnt before
applied on the image? Justify your answer?
b. Can you suggest the role of machines in agriculture? How do they contribute in the rapid
development of the country programs of transformation and modernization of agriculture?
Knowing different stages of growing plants activities, suggest which stages mostly benefit the
use of technology!
Plan it! To get started, brainstorm about your prior knowledge on applications of physics in
agriculture and try to suggest answers to questions given above based on your understanding.
3.1 ATMOSPHERE AND ITS CONSTITUENTS
3.1.1 Atmosphere
Activity 3.1: How the atmosphere protect life on the earth
a. Brainstorm and write short notes on constituents of atmosphere and explain clearly how the
atmosphere of Earth protects life on earth.
b. Why should you care about protecting the atmosphere and minimise the long-term changes in the
climate?
c. What can be the use of atmospheric knowledge in evaluating and improving agricultural
activities?
The atmosphere of earth is the layer of gases, commonly known as air that surrounds the earth. This
layer of gases is retained by Earth's gravity. The atmosphere of Earth protects life on Earth by
absorbing ultraviolet solar radiations that cause cancers and other diseases, warming the surface
through heat retention (greenhouse effect) and reducing temperature extremes between day and
night. It also contain the oxygen which human beings, animals and plants are using, The atmospheric
knowledge can be helpful in evaluating and improving the quality of soils and agricultural products
as well as the technological processes.
3.1.2 Composition of the Atmosphere
The atmosphere is composed of a mixture of several gases in differing amounts. The permanent
gases whose percentages do not change from day to day are nitrogen, oxygen and argon. By volume,
dry air contains 78.0% nitrogen, 21% oxygen, 0.9% argon, 0.04% carbon dioxide, and small
amounts of other gases called trace gases 0.1% as shown in Fig.3.2
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Gases like carbon dioxide, nitrous oxides, methane, and ozone are trace gases that account for about
a tenth of one percent of the atmosphere.
Fig.3. 2Composition of the atmosphere
Air also contains a variable amount of water vapor, on average around 1% at sea level, and 0.4%
over the entire atmosphere. Water vapor is unique in that its concentration varies from 0-4% of the
atmosphere depending on where you are and what time of the day it is. In the cold, dry Arctic
regions water vapor usually accounts for less than 1% of the atmosphere, while in humid, tropical
regions water vapor can account for almost 4% of the atmosphere. Water vapor content is very
important in predicting weather.
Air content and atmospheric pressure vary at different layers, and air suitable for use in
photosynthesis by terrestrial plants and breathing of terrestrial animals is found only in earth's
troposphere.
The composition of the atmosphere, among other things, determines its ability to partly absorb and
transmit sunlight radiations and trap infrared radiations, leading to potentially minimise the long-
term changes in climate.
3.1.3 Layers of the atmosphere.
Activity 3.2 Classifying layers of the atmosphere.
Materials For class demonstration:
Chalk board or dry erase board mounted on a wall
Chalk or dry erase marker
2-meter piece of string
1000 ml (1 litre) graduated cylinder
Four bags of fish gravel or coloured sand (different colours)
Procedures
Case1:
1. Use a model to explore how far the earth's atmosphere extends above the surface of the earth and
learn about the thickness of the different layers of the atmosphere.
2. How far do you think the atmosphere extends above us? Tie a dry eraser marker or a piece of
chalk to one end of the string. Standing next to the board, place your foot on the free end of the
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string and draw an arc on the board with a radius of about 1.2 m. Your foot represents the center
of the earth. The arc represents the surface of the Earth.
Fig.3. 3A person demonstrating the layers of the atmosphere
3. Suggest how far the earth's atmosphere would extend above the surface in this drawing. Mark
your suggestions on the board above the chalk/marker line. Note that it is found that over 90% of
the earth’s atmosphere is within about 12km of the earth’s surface. The distance from the centre of
the earth to its surface equals about 6361 km.
Case 2:
1. Use a 1000 ml (1 litter) graduated cylinder and represent the layers by using the following
amounts of fish gravel or coloured sand found in the photo and table below.
2. Choose what colour you want for each atmospheric layer. Keep in mind these are relative
proportions and not exact points of departure for the different layers. In this scale model, each
millilitre of volume represents one kilometre of atmosphere layer thickness (for example, the
troposphere is 10 km thick and is represented by 10 ml of sand or gravel in the graduated
cylinder).
Fig.3. 4: Color coding represented in cylinder with the corresponding layers
Atmospheric Layer Color Code Thickness Top of Layer
Troposphere Color 1 10 ml 10
Stratosphere Color 2 40 ml 50
Mesosphere Color 3 35 ml 85
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Thermosphere Color 4 915 ml 1000
Table 3. 1: Atmospheric layers with color code and thickness
Questions
1. What atmospheric layers are represented by the different colors?
2. What atmospheric layer do we live in?
3. How much thicker is the stratosphere compared to the troposphere?
4. How much thicker is the thermosphere compared to all the other layers combined?
5. Where in this model would you expect to find clouds?
6. Where in this model would you expect to find mounts Everest and Kalisimbi?
7. Where in this model would you expect to find a satellite?
8. Where in this model would you expect to find the space shuttle?
9. Where in this model is the ozone layer?
Earth's atmosphere has a series of layers, each with its own specific characteristics and properties.
Moving upward from ground level, these layers are named the troposphere, stratosphere,
mesosphere, thermosphere and exosphere.
The above activity demonstrates the relative thickness of the thin section of the atmosphere that
includes the troposphere and stratosphere. These layers are essential to all life on Earth.
Over 99% of the mass of the Earth's atmosphere is contained in the two lowest layers: the
troposphere and the stratosphere. Most of the Earth's atmosphere (80 to 90%) is found in the
troposphere, the atmospheric layer where we live (Cunningham & William, 2000).
This layer, where the Earth's weather occurs, is within about 10 km of the Earth's surface. The
stratosphere goes up to about 50 km. Gravity is the reason why atmosphere is more dense closer to
the Earth's surface.
Fig.3. 5: Illustration of layers from the core to the atmosphere
While we may think of the atmosphere as a vast ocean of air around us, it is very thin relative to the
size of the earth. The "thickness" of the atmosphere, or the distance between the earth's surface and
the "top" of the atmosphere, is not an exact measure. Although air is considered as a fluid, it does not
have the same well-defined surface as water does. The atmosphere just fades away into space with
increasing altitude.
Description of layers of earth's atmosphere:
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a. Troposphere
This is the lowest layer of our atmosphere starting at ground level; it extends upward to about 10 km
above the sea level. We live in the troposphere, and nearly all weather occurs in this lowest layer.
Most clouds appear here, mainly because 99% of the water vapor in the atmosphere is found in the
troposphere. Air pressure drops and temperatures get colder, as you climb higher in the troposphere.
b. Stratosphere
The stratosphere extends from the top of the troposphere to about 50 km above the ground. The
infamous ozone layer is found within the stratosphere. Ozone molecules in this layer absorb high-
energy ultraviolet (UV) light from the sun, converting the ultraviolet energy into heat.
Unlike the troposphere, the stratosphere actually gets warmer the higher you go! That trend of rising
temperatures with altitude means that air in the stratosphere lacks the turbulence and updrafts of
the troposphere beneath. Commercial passenger jets fly in the lower stratosphere, partly because this
less-turbulent layer provides a smoother ride.
c. Mesosphere
It extends upward to a height of about 85 km above our planet. Most meteors burn up in the
mesosphere. Unlike the stratosphere, temperatures once again grow colder as you rise up through the
mesosphere. The coldest temperatures in earth's atmosphere, about -90° C, are found near the top
of this layer. The air in the mesosphere is far too thin to breathe; air pressure at the bottom of this
layer is well below 1% of the pressure at sea level, and continues dropping as you go higher.
d. Thermosphere
High-energy X-rays and ultraviolet radiations from the Sun are absorbed in the thermosphere,
raising its temperature to hundreds or at times thousands of degrees.
Many satellites actually orbit Earth within the thermosphere! Variations in the amount of energy
coming from the Sun exert a powerful influence on both the height of the top of this layer and the
temperature within it.
Because of this, the top of the thermosphere can be found anywhere between 500 km and 1 000 km
above the ground. Temperatures in the upper thermosphere can range from about 500 ° C to
2 000 °C or even higher.
e. Exosphere
Although some experts consider the thermosphere to be the uppermost layer of our atmosphere,
others consider the exosphere to be the actual "final frontier" of Earth's gaseous envelope. As you
might imagine, the "air" in the exosphere is very thin, making this layer even more space-like than
the thermosphere.
In fact, air in the exosphere is constantly "leaking" out of earth's atmosphere into outer space. There
is no clear-cut upper boundary where the exosphere finally fades away into space. Different
definitions place the top of the exosphere somewhere between 100 000 km and 190 000 km above
the surface of earth. The latter value is about halfway to the moon!
f. Ionosphere
The ionosphere is not a distinct layer like the others mentioned above. Instead, the ionosphere is a
series of regions in parts of the mesosphere and thermosphere where high-energy radiation from the
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sun has ionized atoms and molecules. The ions formed in this way are responsible of the naming of
this region as the ionosphere and endowing it with some special properties.
Activity 3.3 Classifying layers of the atmosphere.
Observe scale models of the atmosphere on fig.3.3 below and its layers. Note the height of earth's
atmosphere as compared to the size of the planet overall and the relative thickness of each of the four
main layers of the atmosphere. Interpret the graph and Use it to answer questions below:
Fig.3. 6: Layers of the atmosphere.
Questions:
a) Outline the economic activities taking place in the layers represented above?
b) Why is it very important to have ozone layer in the layers close to the earth surface?
c) Explain why it is advisable to travel in troposphere and stratosphere than in other layers of the
atmosphere?
d) Explain clearly why the rocket and aeroplanes decide to move in the corresponding layers of the
atmosphere?
3.1.4 Checking my progress
1. Use the fruit question suggested in the procedure and respond in writing or with a picture instead
of simply orally in class. Think of the fruit as the size of the Earth and the skin of the fruit represents
the thickness of the atmosphere. Make a labelled diagram in your note book illustrating the most
important point of the lesson and the reason why the atmosphere is considered as the skin of the
fruit?
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2. Imagine that you are in an orbit around a planet one half the size and mass of the Earth. Explain
how I would expect the atmosphere of the new planet to be different from my planet?
3. What is the structure and composition of the atmosphere?
4. How does solar energy influence the atmosphere?
5. How does the atmosphere interact with land and oceans?
6. Outline two most important layers that are essential to all life on earth? Explain clearly to support
your answer.
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3.2 HEAT AND MASS TRANSFER
3.2.1 Modes of Heat Transfer
Activity 3.4: Describing the different modes of heat transfer in the atmosphere
Brainstorm on modes of heat transfer and explain clearly how each affects agricultural activities?
Heat transfer is concerned with the exchange of thermal energy through a body or between bodies
which occurs when there is a temperature difference.
When two bodies are at different temperatures, thermal energy transfers from the one with higher
temperature to the one with lower temperature. Naturally heat transfers from hot to cold.
A small amount of the energy that was directed towards the earth from the sun is absorbed by the
atmosphere, a larger amount (about 30%) is reflected back to space by clouds and the Earth's surface,
and the remaining is absorbed at the planet surface and then partially released as heat.
Energy is transferred between the Earth's surface and the atmosphere in a variety of ways,
including radiation, conduction, and convection. The figure below uses a camp stove to summarize
the various mechanisms of heat transfer. If you were standing next to the camp stove, you would be
warmed by the radiation emitted by the gas flame. A portion of the radiant energy generated by the
gas flame is absorbed by the frying pan and the pot of water.
By the process of conduction, this energy is transferred through the pot and pan. If you reached for
the metal handle of the frying pan without using a potholder, you would burn your fingers! As the
temperature of the water at the bottom of the pot increases, this layer of water moves upward and is
replaced by cool water descending from above. Thus convection currents that redistribute the newly
acquired energy throughout the pot are established.
Fig.3. 7: Camp stove to summarize the various mechanisms of heat transfer.
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As in this simple example using a camp stove, the heating of the Earth's atmosphere involves
radiation, conduction, and convection, all occurring simultaneously. A basic theory of meteorology is
that the Sun warms the ground and the ground warms the air. This activity focuses on radiation, the
process by which the Sun warms the ground. Energy from the Sun is the driving force behind
weather and climate.
Quick check 3.1
What do trees, snow, cars, horses, rocks, centipedes, oceans, the atmosphere, and you have in
common?
Each one is a source of radiation to some degree. Most of this radiation is invisible to humans but
that does not make it any less real.
Radiation is the transfer of energy by electromagnetic waves. The transfer of energy from the Sun
across nearly empty space is accomplished primarily by radiation. Radiation occurs without the
involvement of a physical substance as the medium. The Sun emits many forms of electromagnetic
radiation in varying quantities.
Fig.3. 8: The spectrum of electromagnetic radiations emitted by the sun
About 43% of the total radiant energy emitted from the Sun is in the visible part of the spectrum. The
bulk of the remainder lies in the near-infrared (49%) and ultraviolet (7%) bands. Less than 1% of
solar radiation is emitted as x-rays, gamma rays, and radio waves.
A perfect radiating body emits energy in all possible wavelengths, but the wave energies are not
emitted equally in all wavelengths; a spectrum will show a distinct maximum in energy at a
particular wavelength depending upon the temperature of the radiating body. As the temperature
increases, the maximum radiation occurs at shorter wavelengths.
The hotter the radiating body, the shorter the wavelength of maximum radiation. For example, a very
hot metal rod will emit visible radiation and produce a white glow. On cooling, it will emit more of
its energy in longer wavelengths and will glow a reddish color. Eventually no light will be given off,
but if you place your hand near the rod, the infrared radiation will be detectable as heat.
The amount of energy absorbed by an object depends upon the following:
The object's absorptivity, which, in the visible range of wavelengths, is a function of its color
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The intensity of the radiation striking the object
Every surface on Earth absorbs and reflects energy at varying degrees, based on its color and texture.
Darker-colored objects absorb more visible radiation, whereas lighter-colored objects reflect more
visible radiation. These concepts are clearly discussed in unit two.
3.2.2 Environmental heat energy and mass transfer
Fig.3. 9: Illustration of interactions of solar radiations with different constituents of the atmosphere.
Practically all of the energy that reaches the earth comes from the sun. Intercepted first by the
atmosphere, a small part is directly absorbed, particularly by certain gases such as ozone and water
vapor. Some energy is also reflected back to space by clouds and the earth's surface.
In the atmosphere, convection includes large- and small-scale rising and sinking of air masses..
These vertical motions effectively distribute heat and moisture throughout the atmospheric column
and contribute to cloud and storm development where rising motion occurs) and dissipation where
sinking motion occurs.
3.2.3 Water vapour in the atmosphere.
Activity3.5: Impact of water vapor in agricultural activities
1. Brainstorm on water vapor in the atmosphere and explain clearly how it impacts on agricultural
activities?
2. Does water vapor play an important role in the atmosphere? Justify your answer with clear
reasons.
When water vapor condenses onto a surface, a net warming occurs on that surface. The water
molecule brings heat energy with it. In turn, the temperature of the atmosphere drops slightly. In the
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atmosphere, condensation produces clouds, fog and precipitation (usually only when facilitated by
cloud condensation nuclei).
The role of water vapor in the atmosphere
Water vapor plays a dominant role in the radiative balance and the hydrological cycle. It is a
principal element in the thermodynamics of the atmosphere as it transports latent heat and
contributes to absorption and emission in a number of bands. It also condenses into clouds that
reflect and adsorb solar radiation, thus directly affecting the energy balance.
In the lower atmosphere, the water vapor concentrations can vary by orders of magnitude from place
to place.
3.2.4 Variation in Atmospheric Pressure
Activity 3.6
Brainstorm on the atmospheric pressure and explain clearly how variation of atmospheric pressure
impact on agricultural activities?
Variation with height or vertical variation: The pressure depends on the density or mass of the
air. The density of air depends on its temperature, composition and force of gravity. It is observed
that the density of air decreases with increase in height so the pressure also decreases with increase in
height.
Horizontal variation of pressure: The horizontal variation of atmospheric pressure depends on
temperature, extent of water vapor, latitude and land and water relationship.
Factors affecting atmospheric pressure:
1. Temperature of air
2. Altitude
3. Water vapor in air
4. Gravity of the earth.
Effect of atmospheric pressure in agricultural activities
The pressure exerted by the atmosphere of the earth’s surface is called atmospheric pressure.
Generally, in areas of higher temperature, the atmospheric pressure is low and in areas of low-
temperature the pressure is high. Atmospheric pressure has no direct influence on crop growth. It
is, however an important parameter in weather forecasting.
3.2.5 Air density and water vapour with altitude
Activity 3.7: Effect of air density in the atmosphere
Brainstorm on air density and explain clearly its affects in the earth’s atmosphere?
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The density of air (air density) is the mass per unit volume of earth's atmosphere. Air density, like
air pressure, decreases with increasing altitude. It also changes with variation in temperature and
humidity. At sea level and at 15 °C air has a density of approximately 1.225 kg/m3.
Air density and the water vapor content of the air have an important effect upon engine performance
and the takeoff characteristics of air-craft. Some of the effects these two factors have upon engine
takeoff, and the methods for computing these elements from a meteorological standpoint.
Pressure altitude, density altitude, vapor pressure, and specific humidity in the atmosphere are
determined using a Density Altitude Computer.
Pressure altitude: Pressure altitude is defined as the altitude of a given atmospheric pressure in the
standard atmosphere. The pressure altitude of a given pressure is, therefore, usually a fictitious
altitude, since it is equal to true altitude only rarely, when atmospheric conditions between sea level
and the altimeter in the aircraft correspond to those of the standard atmosphere. Aircraft altimeters
are constructed for the pressure-height relationship that exists in the standard atmosphere.
3.2.6 Checking my progress
1. Why does atmospheric pressure change with altitude?
2. The graph below gives an indication of how pressure varies non-linearly with altitude. Use the
graph to answer the following questions:
Fig.3. 10: A graph of altitude vs pressure
a) Explain what happens to pressure if the altitude reduces?
b) Estimate the atmospheric pressure when someone is at an altitude of 40 km above sea level.
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3.3 PHYSICAL PROPERTIES OF SOIL
Practical Activity 3.8: How the surface of earth reflects and absorbs heat
Perform the activity to investigate how different surfaces of the earth reflect and absorb heat and
apply this knowledge to real-world situations. It justifies that the physical characteristics of the
Earth's surface affect the way that surface absorbs and releases heat from the Sun.
Materials needed in demonstration
Three pie pans or dishes Dark potting soil
Light-colored sand or perlite Water
Three thermometers Reflector lamp with incandescent light bulb
Watch with a second hand Graph paper
Colored pencils Heating and Cooling Data Table
Procedures
1. a) Brainstorm on the already known concepts about how the color and type of material affects how
hot it gets in the sunshine. Try to think about these questions. When it is a hot day, what color shirt
would you wear to keep cool and why? During the summer, what would it feel like to walk on gravel
with no shoes?
b) In performing activity, explore how different types of surfaces found at the earth's surface (such as
sand, soil, and water) heat up when the sun's energy reaches them, and how they cool down when out
of the sunshine.
c) Note that this experiment uses materials to model sunshine and earth materials. Observe the
materials and realize how each material relates to the earth system. (The lamp represents the sun in
this model. The sand represents beaches, sand dunes, and rocks. The potting soil represents large
areas of soil outdoors. And the water represents lakes, rivers, and the ocean.)
2. Fill the pie pans to the same level, one with dark soil, one with light sand, and one with water.
3. Place the pie pans on a table or desk and position the lamp about 30.48 cm above them. (Do not
turn on the lamp yet.)
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Fig.3. 11: Arrangement of pie pans to investigate the absorption of solar radiation.
4. Place a thermometer into each pie pan, with the bulb just under the surface of the substance (soil,
sand, or water) in the pan.
5. Use data table and explain how the tables relate to the experimental design.
6. Record the temperature right before they turn on the lamp (Time = 0), entering the number into
their data table.
7. Turn on the lamp and instruct students to record the temperature every minute in the three pie pans
for ten minutes.
8. After ten minutes, turn the lamp off and instruct students to continue recording temperatures every
minute for ten minutes.
9. Graph the temperature data using graph paper and colored pencils. Write a caption for your graph
that describes how the three different materials change in temperature over time.
10. Compare your graph to that of your colleagues and brainstorm on your results.
Checking skills Questions
1. Which material absorbed more heat in the first ten minutes?
2. Which material lost the most heat in the last ten minutes?
3. Imagine that it is summer and that the Sun is shining on the ocean and on a stretch of land.
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a. Which one will heat up more during the day?
b. Which one will cool more slowly at night? Explain.
4. Imagine three cities in the desert, all at about the same altitude and latitude. Which city would
likely have the highest average summer air temperature and why?
One city (A) is surrounded by a dark-colored rocky surface.
Another city (B) is surrounded by a light-colored sandy surface.
The third city (C) is built on the edge of a large man-made desert lake.
5. The Earth's surface tends to lose heat in winter. Which of the above cities would have the warmest
average winter temperature? Why?
6. Since the Sun is approximately 93 million miles from the Earth and space has no temperature, how
do we get heat from the Sun?
Physical properties of a soil that affect a plant's ability to grow include: Soil texture, which affects
the soil's ability to hold onto nutrients (cation exchange capacity) and water. Texture refers to the
relative distribution of the different sized particles in the soil. It is a stable property of soils and,
hence, is used in soil classification and description.
Soil structure, which affects aeration, water-holding capacity, drainage, and penetration by roots
and seedlings, among other things. Soil structure refers to the arrangement of soil particles into
aggregates and the distribution of pores in between. It is not a stable property and is greatly
influenced by soil management practices.
3.3.1 Soil texture
Practical Activity3.9:
Soil texture is determined by three proportions of the soil. Brainstorm and try to answer questions
using knowledge gained.
a. Outline three proportions of the soil?
b. What does the underlined word mean?
Soil texture, or the 'feel' of a soil, is determined by the proportions of sand, silt, and clay in the soil.
When they are wet, sandy soils feel gritty, silky soils feel smooth and silky, and clayey soils feel
sticky and plastic, or capable of being moulded. Soils with a high proportion of sand are referred to
as 'light', and those with a high proportion of clay are referred to as 'heavy'.
The names of soil texture classes are intended to give you an idea of their textural make-up and
physical properties. The three basic groups of texture classes are sands, clays and loams.
A soil in the sand group contains at least 70% by weight of sand. A soil in the clay group must
contain at least 35% clay and, in most cases, not less than 40%. A loam soil is, ideally, a mixture of
sand, silt and clay particles that exhibit light and heavy properties in about equal proportions, so a
soil in the loam group will start from this point and then include greater or lesser amounts of sand,
silt or clay.
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3.3.2 Soil structure
Activity3.10:
a) It is known that soil structure contains soil particles and pores and is classified under physical
properties of soil. Brainstorm and write short notes on soil structure.
Use the knowledge gained in part (a) above to answer questions in part (b).
b) (i) List the elements found in soil particles.
(ii) What do the underlined words mean?
(iii) Explain the role of pores in soil structure that improves capillary action in plant growth.
Structure is the arrangement of primary sand, silt and clay particles into secondary aggregates called
peds or structural units which have distinct shapes and are easy to recognize. These differently
shaped aggregates are called the structural type.
There are 5 basic types of structural units:
Platy: Plate-like aggregates that form parallel to the horizons like pages in a book. This type of
structure may reduce air, water and root movement.
Blocky: Two types--angular blocky and sub angular blocky. These types of structures are
commonly seen in the B horizon. Angular is cube-like with sharp corners while sub angular
blocky has rounded corners.
Prismatic: Vertical axis is longer than the horizontal axis. If the top is flat, it is referred to as
prismatic. If the top is rounded, it is called columnar.
Granular: Peds are round and pourous, spheroidal. This is usually the structure of A horizons.
Structureless: No observable aggregation or structural units.
Good soil structure means the presence of aggregations which has positive benefits for plant growth.
These benefits arise from the wider range of pore sizes which result from aggregation.
The nature of the pore spaces of a soil controls to a large extent the behavior of the soil water and the
soil atmosphere. It influences the soil temperature. All these affect root growth, as does the
presence of soil pores of appropriate size to permit root elongation. Favorable soil structure is
therefore crucial for successful crop development. The destruction of soil structure may result in a
reduction in soil porosity and/or change to the pore size distribution.
Soil structure refers to the arrangement of soil particles (sand, silt and clay) and pores in the soil and
to the ability of the particles to form aggregates.
Aggregates are groups of soil particles held together by organic matter or chemical forces.
Pores are the spaces in the soil. The pores between the aggregates are usually large (macro pores),
and their large size allows good aeration, rapid infiltration of water, easy plant root penetration, and
good water drainage, as well as providing good conditions for soil micro-organisms to thrive. The
smaller pores within the aggregates or between soil’s particles (micro pores) hold water against
gravity (capillary action) but not necessarily so tightly that plant cannot extract the water.
A well-structured soil forms stable aggregates and has many pores (Fig.3.12 A). it is friable, easily
worked and allows germinating seedlings to emerge and to quickly establish a strong root system. A
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poorly structured soil has either few or unstable aggregates and few pore spaces (Fig.3.12 B). This
type of soil can result in unproductive compacted or waterlogged soils that have poor drainage and
aeration. Poorly structured soil is also more likely to slake and to become eroded.
Fig.3. 12: Different soil structures: well structured and poorly structured soil.
3.3.3 Checking my progress:
1. Explain the physical properties of Soil and explain clearly how each impact agricultural activities?
2. (a)Explain how the weathering of rocks contributes to soil formation.
(b) Explain the following terms as used in the context of soil and plant growth.
(i) Well structured soil (ii) Poor structured soil
(c) The following table shows the water content of three soil samples. Use the table to answer
questions that follows:
Soil Sample % Water in soil sample 1 % Water at soil sample 2
A 6 2
B 24 12
C 30 22
Analytical Questions:
i. What is the percentage of available water in sample A?
ii. Which sample would be the most suitable for a crop suffering a drought during the growing season?
iii. Which sample would be the most suitable for a crop growing during a rainy season?
(d) Describe an experiment to compare the capillarity of two contrasting soils.
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3.4 MECHANICAL WEATHERING
3.4.1 Concepts of mechanical weathering
Laboratory Activity 3.11: Exploring Mechanical Weathering
Mechanical rock weathering is an important part of the formation of both soils and new rocks, and an
important part of the entire rock cycle. The activity explores what causes rocks to break down.
Materials:
• Coffee can with lid • Rocks
• Dark-coloured construction paper
Fig.3. 1Coffee can with lid
Procedures
Place a handful of rocks on a piece of dark-coloured construction paper. Observe the rocks and take
notes on their appearance. Place the rocks in a coffee can. Put the lid on the can and shake the can
forcefully for 2 minutes, holding the lid tightly shut. Pour the rocks onto the construction paper.
Observe them and take notes on any changes in their appearance.
Use the skills gained above to answer the following questions:
a) What happened to the rocks and why?
b) What forces in nature might affect rocks in similar ways?
c) Briefly explain what causes mechanical weathering?
Earth’s surface is constantly changing. Rock is integrated and decomposed, moved to lower
elevations by gravity, and carried away by water, wind, or ice. When a rock undergoes mechanical
weathering, it is broken into smaller and smaller pieces of sediment and dissolved minerals; each
retaining the characteristics of the original material. The result is many small pieces from a single
large one.
Weathering takes place in two ways: physical weathering and chemical weathering. Physical and
chemical weathering can go on at the same time. Weathering is thus the response of Earth’s materials
to change environment. Weathering is the first step in the breakdown of rock into smaller fragments.
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This process is critical to the formation of landscapes and many other geological processes. Our
discussion will focus on mechanical weathering.
Mechanical weathering is the physical breaking up of rocks into smaller pieces.
3.4.2 Causes of mechanical weathering
a) Temperature change
Activity 3.12: Effects of temperature on mechanical weathering
a) Brainstorm on the effects of temperature in mechanical weathering and explain clearly its
impacts on soil formation and agricultural activities?
b) Explain how thermal expansion and contraction affect mineral composition?
As the water evaporates, the salt is left behind. Over time, these salt deposits build up, creating
pressure that can cause rocks to split and weaken. Temperature changes also affect mechanical
weathering. As temperatures heat up, the rocks themselves expand.
Fig.3. 2 Illustration of mechanical weathering
Temperature is an essential part of rock creation, modification and destruction. Heating a rock causes
it to expand, and cooling causes it to contract. Repeated swelling and shrinking of minerals that have
different expansion and contraction rates should exert some stress on the rock’s outer shell.
Thermal expansion and contraction of minerals
Thermal expansion is the tendency of matter to change in shape, area, and volume in response to a
change in temperature. Thermal expansion due to the extreme range of temperatures can shatter
rocks in desert environments. Temperature is a monotonic function of the average molecular kinetic
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energy of a substance. When a substance is heated, the kinetic energy of its molecules increases.
Thus, the molecules begin vibrating more and usually maintain a greater average separation.
Materials which contract with increasing temperature are unusual; this effect is limited in size, and
only occurs within limited temperature ranges. The relative expansion (also called strain) divided by
the change in temperature is called the material's coefficient of thermal expansion and generally
varies with temperature.
Materials expand or contract when subjected to changes in temperature. Most materials expand when
they are heated, and contract when they are cooled. When free to deform, concrete will expand or
contract due to fluctuations in temperature.
Concrete expands slightly as temperature rises and contracts as temperature falls. Temperature
changes may be caused by environmental conditions or by cement hydration.
Thermal expansion and contraction of concrete varies primarily with aggregate type (shale,
limestone, siliceous gravel and granite), cementitious material content, water cement ratio,
temperature range, concrete age, and ambient relative humidity. Of these factors, aggregate type has
the greatest influence on the expansion and contraction of concrete.
Quick Check 3.2
a) How does climate affect the rate of weathering?
b) What is the process that breaks down rocks?
Effects of temperature and moisture changes on weathering
At high elevations, cold night time temperatures during much of the year can produce relentless
freeze-thaw cycles. This process explains the presence of broken boulders and stony fragments that
litter mountaintops. And, the minerals in volcanic rock that formed at the highest temperatures and
pressures are the most vulnerable to chemical weathering at Earth's surface.
In many locations, changes in temperature and moisture content of the environment cause significant
physical weathering. When rock is warmed, it expands; when it cools, it contracts. In some regions,
rocks are heated to relatively high temperatures during the day and then cooled to much lower
temperatures during the night. The constant expansion and contraction of the rocks may result in
pieces being broken off.
Temperature also affects the land as the cool nights and hot days always cause things to expand and
contract. That movement can cause rocks to crack and break apart.
The most common type of mechanical weathering is the constant freezing, and thawing of water. In
liquid form, water is capable of penetrating holes, joints, and fissures within a rock. As the
temperature drops below zero celcius, this water freezes. Frozen water expands compared to its
liquid form. The result is that the holes and cracks in rocks are pushed outward. Even the strongest
rocks are no match for this force.
As temperatures heat up, the rocks themselves expand. As the temperatures cool down, rocks
contract slightly. The effect can be the weakening of the rock itself which induces mechanical
weathering. It breaks rock into smaller pieces. These smaller pieces are just like the bigger rock, but
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smaller. That means the rock has changed physically without changing its composition. The smaller
pieces have the same minerals, in just the same proportions as the original rock.
b) Ice wedging
There are many ways that rocks can be broken apart into smaller pieces. Ice wedging is the main
form of mechanical weathering in any climate that regularly cycles above and below the freezing
point (Fig.3.13). Ice wedging works quickly, breaking apart rocks in areas with temperatures that
cycle above and below freezing in the day and night.
Fig.3. 13Ice wedging.
Explanation of figure 3.14: (A) water seeps into cracks and fractures in rock, (B) when the water freezes, it expands
about 9% in volume, which wedges apart the rock, (C) with repeated freeze cycles, rock breaks into pieces.
Ice wedging breaks apart so much, rocks with large piles of broken rock are seen at the base of a
hillside, as rock fragments separate and tumble down. Ice wedging is common in Earth’s polar
regions and mid latitudes, and also at higher elevations in the mountains.
Water has the unique property of expanding about 9% when it freezes. This increase in volume
occurs because, as ice form, the water molecules arrange themselves into a very open crystalline
structure. As a result, when water freezes, it expands and exerts a tremendous outward force. This
can be verified by completely filling a container with water and freezing it.
After many freezing cycle, the rock is broken into pieces. This process is called frost wedging also
as known as Freeze-thaw weathering as shown in Fig.3.13. This occurs when water gets into the
small holes and gaps in rocks. If the water in the gap freezes, it expands, splitting the existing gaps
into wider cracks. When the water thaws, the wider gaps allow even more water to enter the rock and
freeze. Frost wedging can repeat over months or years, turning microscopic gaps in the rock into
large cracks.
Ice has more volume than liquid water, so the cracks are forced wider. Then, more water accumulates
in the cracks the next day, which freeze at night to widen the cracks further. When this happens
repeatedly, the rock eventually breaks apart along the crevices.
Frost heaving, a similar process to frost wedging, occurs when a layer of ice forms under loose rock
or soil during the winter, causing the ground surface to bulge upward. When it melts in the spring,
the ground surface collapses.
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c) Abrasion
Activity 3.14: Importance of abrasion in real life situations
With the help of knowledge gained in the concepts above, explain how abrasion is formed and
suggest its importance in real life situations?
The word ‘abrasion’ literally means scraping of the surface of an object. This is exactly what
happens with abrasion of rocks. Weathering by abrasion is responsible for the creation of some of the
largest deserts in the world. The rock’s surface is exposed to blown sands - high velocity winds
which blow throughout the day while carrying large sand particles.
The sand blasts against the surfaces of the rocks, undercutting and deflating them. As a result,
smaller rock particles are formed, which when exposed to further sand abrasion become sand
particles themselves.
Abrasion makes rocks with sharp or jagged edges smooth and round. If you have ever collected
beach glass or cobbles from a stream, you have witnessed the work of abrasion (Fig.3.14 below).
Rocks on a beach are worn down by abrasion as passing waves cause them to strike each other.
Fig.3. 14 Smooth round rocks
In abrasion, one rock bumps against another rock. The following are the causes of abrasion;
Gravity causes abrasion as a rock tumbles down a mountainside or cliff.
Moving water causes abrasion as particles in the water collide and bump against one another.
Strong winds carrying pieces of sand can sandblast surfaces.
Ice in glaciers carries many bits and pieces of rock. Rocks embedded at the bottom of the
glacier scrape against the rocks.
Therefore abrasion occurs when the surface of rocks is exposed to water or wind. These elements can
carry tiny particles of sediment or rock that then collide against the rock's surface. When these
particles rub against the rock's surface, they break off tiny pieces of the rock. Over time, abrasion can
wear down and smooth extremely large sections of the rock.
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d) Biological activity
Weathering is also accomplished by the activities of organisms, including plants, burrowing animals,
and humans. Plant roots in search of minerals and water grow into fractures, and as the roots grow
they wedge the rock apart
Burrowing animals further break down the rock by moving fresh material to the surface, where
physical and chemical process can more effectively attack it. Decaying organisms also produce acids,
which contribute to chemical weathering
3.4.3 Factors influencing the type and rate of rock weathering
Activity3.15:
Brainstorm and classify clearly the factors affecting the rate of weathering?
Several factors influence the type and rate of rock weathering. By breaking a rock into smaller
pieces, the amount of surface area exposed to chemical weathering is increased. The presence or
absence of joints can be significant because they influence the ability of water to penetrate the rock.
Other important factors include the mineral makeup of rocks and climate.
a) Climate
The amount of water in the air and the temperature of an area are both part of an area’s climate.
Moisture speeds up chemical weathering. Weathering occurs fastest in hot, wet climates. It occurs
very slowly in hot and dry climates. Without temperature changes, ice wedging cannot occur. In very
cold, dry areas, there is little weathering.
b) Surface area
Most weathering occurs on exposed surfaces of rocks and minerals. The more surface area a rock
has, the more quickly it will weather. When a block is cut into smaller pieces, it has more surface
area. So, therefore, the smaller pieces of a rock will weather faster than a large block of rock
c) Rock composition
Headstones of granite, which is composed of silicate minerals, are relatively resistant to chemical
weathering. The minerals that crystallize first form under much higher temperatures than those which
crystallize last. Consequently, the early formed minerals are not as stable at Earth’s surface, where
the temperatures are different from the environment in which they formed. Olivine crystalizes first
and is therefore the least resistant to chemical weathering, whereas quartz, which crystallizes last, is
the most resistant.
d) Pollution speeds up weathering
Factories and cars release carbon dioxide and other gases into the air. These gases dissolve in the
rainwater, causing acid rain to form. Acid rain contains nitric and sulfuric acid, causing rocks and
minerals to dissolve faster.
e) Soil erosion and soil deposition
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Activity 3.17: Soil erosion
Look at the figure below that represents soil erosion. Carefully study the figure and answer the
following questions:
Fig.3. 15 The erosive force of wind on an open field.
i. What does the term soil erosion mean?
ii. Write down the two kinds of soil erosion illustrated in the figure above? Which kind of soil
erosion mostly occurs in your home area?
iii. Explain clearly how the kinds of soil erosion outlined in ii) above affects on agricultural
activities?
Soil covers most land surfaces. Along with air and water, it is one of our most indispensable
resources. Soil is a combination of mineral and organic matter.
Soil erosion is a naturally occurring process that affects all landforms. In agriculture, soil erosion
refers to the wearing away of a field's topsoil by the natural physical forces of water and wind or
through forces associated with farming activities.
Erosion is incorporation and transportation of material by a mobile agent, usually water, wind, or
ice.
Erosion whether it is by water and wind, involves three distinct actions – soil detachment, movement
and deposition. Topsoil, which is high in organic matter, fertility and soil life, is relocated elsewhere
"on-site" where it builds up over time or is carried "off-site" where it fills in drainage channels. Soil
erosion reduces cropland productivity and contributes to the pollution of adjacent watercourses,
wetlands and lakes.
Soil erosion can be a slow process that continues relatively unnoticed or can occur at an alarming
rate, causing serious loss of topsoil.
Soil compaction, low organic matter, loss of soil structure, poor internal drainage and soil acidity
problems are other serious soil degradation conditions that can accelerate the soil erosion process.
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Fig.3. 16 The erosive force of water from concentrated surface water runoff.
Deposition is the geological process in which sediments, soil and rocks are added to a landform or
land mass. Wind, ice, and water, as well as sediment flowing via gravity, transport previously eroded
sediment, which, at the loss of enough kinetic energy in the fluid, is deposited, building up layers of
sediment.
3.4.4 Checking my progress
1. The pictures A and B are of two geographical features. Look and carefully study the pictures to
answer questions below.
.
Fig.3. 17 Illustration of geographical features
a) Interpret the images above and Use your observation to suggest names of the corresponding
geographical features in the image above?
b) Do you have such geographical features in your district or neighboring districts? Use your
observation to explain clearly the two geographical features occurring in the image above?
c) Explain the causes for each geographical feature occurring above?
d) Can the geographical features identified above impact agriculture in our communities? Explain
with clear facts to support your decision.
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e) What are moral and ethical issues associated with the geographical features given above?
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3.5 END UNIT ASSESSMENT
3.5.1 Multiple choices questions
For question 1 to 5, choose the letter of the best answer
1. It is known that earth’s atmosphere has a series of layers, each with its own specific characteristics
and properties? The following is the appropriate layer where we live.
A. Thermosphere C. Stratosphere
B. Troposphere D. Mesosphere
2. Consider the following statements:
I. The atmosphere of Earth protects life on Earth by absorbing ultraviolet solar radiation, warming the surface
through greenhouse effect and reducing temperature extremes between day and night.
II. X-rays and ultraviolet radiation from the Sun are absorbed in the thermosphere.
III. The stratosphere extends from the top of the thermosphere to about 50 km above the ground.
Of these statements:
A. I, II, and III are correct. C. I and II are correct but III is wrong
B. I, II and III are wrong D. I and III are wrong but II is correct
3. Agrophysics is defined as
A. The branch of science dealing with study of matter and energy and their mutual relation.
B. The branch of science dealing with communication devices to measure and collect information
about physical conditions in agricultural and natural environments.
C. The branch of natural sciences dealing with the application of physics in agriculture and
environment.
D. None of these
4. Mechanical weathering is caused by
A. Ice wedging, pressure release, plant root growth, and abrasion can all cause mechanical
weathering
B. Mechanical weathering is not formed as the results from changes in temperature and pressure
surrounding rocks.
C. Mechanical weathering is formed as the result of human activities.
D. Both (A) and (C).
E. All statements (A), (B), and (C).
5. Which of the following is the role of the water vapour in the atmosphere?
A. Reducing temperature in the atmosphere
B. Radiative balance and the hydrological cycle
C. None of the above.
D. All of the above.
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3.5.2 Structured Questions
1. Write the missing word or words on the space before each number. For items 1-9
A. ___speeds up chemical weathering.
B. Weathering happens ______ in hot, wet (humid) climates.
C. Weathering occurs very slowly in _______ and ______ climates.
D. Without ________ changes, ice wedging cannot occur
E. In very ________ and ________ areas, there is little weathering.
F. Most weathering occurs on ____________________of rocks and minerals
G. The ________ surface area a rock has, the quicker it will weather.
H. Some minerals resist weathering. _________________ is a mineral that weathers slowly.
I. Rocks made up of minerals such as feldspar, ______, and iron, weather more quickly.
2. If the statement is true, write true. If it is false, change the underlined word or words to
make the statement true.
A. a) Water vapor is very important in predicting weather.
B. Temperature is a reason why atmosphere is more dense close to the earth’s surface.
C. Agrophysics plays an important role in the limitation of hazards to agricultural objects and
environment.
D. Energy is transferred between the earth surface and planet in a variety of ways.
E. As the temperature increases in the atmosphere, the minimum radiation occurs at short
wavelengths.
3. Write a sentence describing the relationship between each pair of terms.
i) Gravity, atmosphere ii) Temperature, rocks.
4. Marry wants to make agrophysics journal. She says, “My journal will be focused on advances in
sensors and communication devices to measure and collect information about physical conditions in
agricultural and natural environments”. Evaluate Marry’s statement.
5. With the help of two clear examples on each, explain clearly how temperature and water vapor
impact agricultural activities using the table.
Terms Impact of temperature and water vapor in
agricultural activities.
1.Temperature
2.Water vapor
6. Complete the chart below. If the left column is blank, give the correct term. If the right column is
blank, give an example of economic activities taking place in the corresponding layer if possible.
Term An example of economic activities taking place in the corresponding layer if
available.
1.Troposphere
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2.Stratosphere
3. Mesosphere
4.
Thermosphere
7. How do climate impact agricultural activities?
8. Explain briefly the role of machines in agriculture in rapid development of the country towards
suitable programs of transformation and modernization of agriculture?
9. Knowing different stages of growing plants in our daily agriculture activities, explain clearly
which stages mostly benefit the use of technology?
10. Cracks in rocks widen as water in them freezes and thaws. How does this affect the surface of
Earth?
11. Name the four factors that can hasten or speed up the process of weathering.
12. How is weathering different from erosion? Think!
13. How can increasing the surface area of rock hasten or speed up the process of weathering Think!
14. Human activities are responsible for enormous amounts of mechanical weathering, by digging or
blasting into rock to build homes, roads, and subways or to quarry stone. Suggest measures that can
be taken to minimize mechanical weathering caused by human activities?
3.5.3 Essay type questions
15. Design and conduct your own research into the influence of surfaces on temperature comparing
earth surfaces that interest them (such as colored soils, dry and wet soils, grass, dry leaves, or
different types of coverings such as plastic or aluminum foil). Compare the data with these new
surfaces compared to the given surfaces (water, light soil, dark soil). Note that the data may not be
comparable due to variations in experimental design, such as differences in light bulb temperature
and height of the lamp.
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UNIT 4: EARTHQUAKES, LANDSLIDES, TSUNAMI, FLOODS AND
CYCLONES.
Fig. 4.1: Illustration of the impact of natural disaster such as earthquakes, tsunami, floods,
landslides, cyclones on human activities and infrastructures.
Key unit Competence
By the end of the unit the learner should be able to relate physics concepts to earthquakes, Tsunami
landslide and cyclone occurrences and impact on environment.
My goals
Anaylse earthquakes, landslides, floods, and tsunami
Describe natural and human made seismic occurrences
Describe earthquake causes as: geological faults, volcanic activity, landslides, mine blasts, and
nuclear weapon tests.
Relate Physics concepts to natural disasters impact.
Explain causes of earthquakes, tsunami, landslide and floods.
Outline impacts of earthquakes on buildings and other structures.
INTRODUCTORY ACTIVITY:
Using the information collected from the above Fig. 4.1, answer the following questions related to
natural disasters due to underground earth’s movements. Your answers have to reflect the role of
Physics in explaining the origin, causes and impact of these natural disasters. Also describe how their
impacts on the environment can be reduced.
- To what extend is the human activities and environment are affected by natural disaster?
- What are the measures to minimize their impacts or prevent them from occurring?
- What makes buildings to collapse during such disturbance? What can be done to minimize the
impact on buildings and other properties?
- What happen to the ocean when such underground disturbances occur?
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By learning this unit, each student will realize the need for better understanding of the basic physics
concepts behind the occurrence of natural disasters such as earthquake, landslide, tsunami, flood and
cyclone. The unit focuses on the physics and dynamic of those natural disasters.
4.1 The earthquake
Activity4.1: Physical concept behind the earthquake.
1. Brainstorm the physics concepts behind the occurrence of earthquakes.
2. Write a summary of the main physics concepts in the occurrence of the earthquake.
An earthquake also known as a quake, tremor or temblor is the shaking or trembling of the
ground caused by the sudden release of energy. This is usually associated with faulting or breaking
of rocks followed by continuing adjustment of their positions with the later resulting in aftershocks.
This continuing shaking or trembling of the ground with unexpected energy is usually associated
with perturbation of ground’s medium in different direction that causes the ground to be compressed
and stretched. The stretching and compression of the ground medium will result in the emission of
waves that propagate in all directions.
During the ground’s shaking, the elastic strain energy is released and waves radiate from where
ground is disturbed. An element of the ground therefore moves in simple harmonic motion.
It is said that earthquakes has created seismic waves. Those waves can range in size from those that
are so weak that they cannot be felt to those that are violent enough to toss people around and destroy
entire cities.
The seismicity or seismic activity of an area refers to the frequency, type and size of earthquakes
experienced over a period of time. The place where an earthquake begins underground is called the
focus or hypocenter, and the area on the earth's surface directly above the hypocenter is called the
epicenter. This epicenter region receives normally the most powerful shock waves.
Fig.4. 2: A region where Earthquakes begin.
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4.1.1 Origin of earthquakes
Earthquake originates from a high pressure region at the hypocenter. This high pressure increases
gradually the temperature and the increase in temperature inside the earth and consequently the
increase in heat finally makes rocks to be in molten state.
As pressure keeps on increasing due to strong heat effect, molten rocks try to get rid of the excess
pressure and explode. The explosion induces elastic energy release at the hypocenter and a wave
spread out as result of the shifting of the plates and internal disturbances. The wave propagates away
from the source. In additional to that, the disturbance that moves away from the hypocenter makes
the earth to vibrate. So quakes are accompanied with shock waves.
To better understand this phenomenon, let take an example a covered sauce pan filled with milk and
heated up. As the pressure increases inside the saucepan, the temperature also increases and the milk
starts to boil. As the milk boils due to increased temperature, the excess pressure in milk eject the
cover of the saucepan and the sound of the boiling milk is heard at a certain distance from where the
phenomenon occurred.
Major earthquakes have generated into tsunamis that destroyed entire cities and affected whole
countries. Relatively minor earthquakes can also be caused by human activity, including extraction
of minerals and the collapse of large buildings.
4.1.2 Intensity of earthquakes
The earthquake size is a quantitative measure of the size of the earthquake at its source. The Richter
magnitude scale measures the amount of seismic energy released by an earthquake.
This magnitude is related to the amount of seismic energy released at the hypocenter of the
earthquake. It is based on the amplitude of the earthquake waves recorded on instruments which have
identical calibrations called seismographs. The magnitude of an earthquake is translated in the
reading on the Richter scale.
The severity of an earthquake can be expressed in terms of both the intensity and magnitude.
However, the two terms are quite different and are often confused.
Intensity is based on the observed effects of ground shaking on people, buildings, and natural
features. It varies from place to place within the disturbed region depending on the location of the
observer with respect to the earthquake’s epicenter.
The amplitude and energy measured by the Richter scale are objective and quantitative while
intensity is more subjective and qualitative as it depends on the judgment of the observers.
Earthquakes are recorded by instruments called seismographs or seismometer and their recordings
produce a seismogram as represented on fig.4.3. The fig. 4.2 shows a typical seismograph used to
measure the magnitude of earthquakes. It has a base that is set firmly on the ground and a heavy
weight that hangs free.
When an earthquake causes the ground to shake, the base of the seismograph shakes too, but the
hanging weight does not. Instead the spring or the string that it is hanging from absorbs all the
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movement. The difference in position between the shaking part of the seismograph and the
motionless part of it is what is recorded.
Fig.4. 3: Instrument used to measure earthquakes: seismographs or seismometer
4.1.3 Measurement of the size of earthquakes
The size of an earthquake depends on the size of the fault and the amount of slip on the fault, but
that’s not something scientists can simply measure since faults are many kilometers deep beneath the
earth’s surface. So how do they measure an earthquake? They analyse the seismograms recorded at
the surface of the earth to determine how large the earthquake was. A typical seismogram is shown
on the Fig.4.3.
Fig.4. 4: intensity or size of Earthquakes.
A short wiggly line that doesn’t wiggle very much means a small earthquake, and a long wiggly line
that wiggles a lot means a large earthquake. The length of the wiggle depends on the size of the fault,
and the size of the wiggle depends on the amount of slip.
4.1.4 Types of earthquake waves
They are two types of earthquakes. Those are body and surface waves
Body waves are subdivided into P waves or Primary waves and S wave or secondary waves. P
and S waves shake each the ground in different ways as they travel through it. The P waves, or
compression waves, alternately compresses and expands medium in the direction of propagation.
They are fastest waves and travel through solids, liquids, or gases.
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The surface waves or S waves are slower than P waves and travel through solids only. They are
shear waves and the direction of propagation of such waves is perpendicular to the direction of
vibration of the medium. The surface waves just travel below or along the ground’s surface and
their side-to-side movement and the rock vibration reduce with depth into the earth. They are the
main cause of damage to buildings.
To understand how this works, let’s compare P and S waves to lightning and thunder. Light travels
faster than sound, so during a thunderstorm you will first see the lightning and then after hear the
thunder. If you are too close to where the lightning happens, the thunder will boom right after the
lightning, but if you are far away from the lightning, you can count several seconds before you hear
the thunder.
4.1.5 Causes of earthquake
The shaking motion of an earthquake is the result of a sudden release of energy. This situation is
observed when stress, building up within rocks of the earth's crust, is released in a sudden jolt. Rocks
crack and slip past each other causing the ground to vibrate. The causes are both natural and man-
made.
Volcanic activity: The combining effects of increase of pressure, temperature and heat inside the
volcano results in volume increase and increase in energy. This makes rocks inside the volcanoes
to be in molten rocks and as the heat keeps on increasing the molten rocks become sticky hot
liquid. As the volume increase further within that sticky liquid it will reach a boiling point and
start ejecting gases at high temperature. The ejection of such gases makes the ground to vibrate
resulting in earthquakes. Finally the molten liquid is ejected out in an explosion. Earthquakes
related to volcanic activity may produce hazards which include ground cracks or deformation.
Nuclear weapon testing: The process of underground nuclear testing is rather straightforward.
The rocks in the surrounding area of the thermonuclear device are scattered by the passage of
explosion shock waves. This sudden release of the elastic strain energy that was stored in the rock
will cause the ground to vibrate.
Underground mining: In mining depending on the amount of materials that are removed from
the ground, people use deep well injection and shift the stress on underlying rocks. At some point
the extractions of minerals will cause the ground to vibrate.
There are other causes such as water pumping, collapse of roofs of caverns or even heavy trucks that
can cause the ground to shake.
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4.1.6 Effects of earthquakes
Activity 4.2: Effects of earthquakes
Fig.4. 5: illustration of impact of earthquakes on human activities.
The above pictures A, B and C describe what happened in a certain region after an earthquake.
Observe them carefully and answer the following questions:
1. In your own words, discuss what you are observing.
2. Think of what people can do before, during and after an earthquake.
The earthquake environmental effects are effects caused by an earthquake on the natural
environment. These include surface faulting, ground deformation and subsidence tsunamis, ground
resonance, landslides and ground failures. They are either directly linked to the earthquake source or
provoked by the ground shaking.
Geological effects such as soil liquefaction, landslides etc., that are related to both surface
deformation, faulting and ground shaking, not only leave permanent imprints in the environment, but
also dramatically affect human lives and infrastructures. Moreover, underwater fault ruptures and
seismically triggered landslides can generate devastating tsunami waves.
Earthquakes environmental effects are categorized into two main types:
Primary effects: which are the surface expression of the seismogenic source (e.g., surface
faulting), normally observed for crustal earthquakes above a given magnitude threshold.
Secondary effects: basically those effects are related to ground. It includes landslides, soil
liquefaction, fires, floods etc. they play an important role in the destructions produced by
earthquakes.
The direct shaking effects as damage or collapse of buildings, bridges, elevated roads, railways,
water towers, water treatment facilities, utility lines, pipelines, electrical generating facilities and
transformer stations , are not the only hazard associated with earthquakes
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Depending on the vulnerability of the affected community, people may lose their lives get
traumatized or become homeless in the aftermath of an earthquake. The table below shows the
Richter magnitude of earthquakes and impacts they have on people and infrastructures.
Richter magnitude Earthquakes effects
0 – 2 Not felt by people
2 – 3 Felt a little by people
3 – 4 Ceiling lights swing
4 – 5 Walls crack
5 – 6 Furniture moves
6 -7 Some buildings collapse
7 – 8 Many buildings destroyed
8 – up Total destruction of buildings, bridges and roads.
Table 4.1: Richter magnitude of earthquakes.
4.1.7 Safety measures on earthquakes
Before an earthquake
You should secure all items that could fall or move and cause injuries or damage (e.g.
bookshelves, mirrors, light fixtures, televisions, computers, hot water heaters etc).
Move beds away from windows and secure any hanging items over beds, other places people sit
or lie.
Protect yourselves: Cover your head and neck with your arms.
Create a strategies plan that you will use to communicate with family members.
Consult a structural engineer to evaluate your home and ask about updates to strengthen areas
that would be weak during an earthquake.
In searching buildings to rent or buy, verify whether its materials have earthquake standards.
During an earthquake
Lay down onto your hands and knees so the earthquake doesn’t knock you down.
Cover your head and neck with your arms to protect yourself from falling debris.
If you are in danger from falling objects, and you can move safely, crawl for additional cover
under a sturdy desk or table.
If no sturdy shelter is nearby, crawl away from windows, next to an interior wall. Stay away from
glass, windows, outside doors and walls, and anything that could fall, such as light fixtures or
furniture.
Hold on to any sturdy covering so you can move with it until the shaking stops.
Stay where you are until the shaking stops. Do not run outside. Do not get in a doorway as this
does not provide protection from falling or flying objects, and you may not be able to remain
standing.
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If you are in bed:
Stay there and Cover your head and neck with a pillow. At night, hazards and debris are difficult
to see and avoid; attempts to move in the dark result in more injuries than remaining in bed.
If you are outside:
If you are outdoors when the shaking starts, move away from buildings, streetlights, and utility
wires. Once in the open, “Drop, Cover, and Hold On.” Stay there until the shaking stops.
If you are in a moving vehicle:
It is difficult to control a vehicle during the shaking. If you are in a moving vehicle, stop as
quickly and safely as possible and stay in the vehicle. Avoid stopping near or under buildings, trees,
overpasses, and utility wires. Proceed cautiously once the earthquake has stopped. Avoid roads,
bridges, or ramps that the earthquake may have damaged.
After an earthquake
When the shaking stops, look around. If the building is damaged and there is a clear path to safety,
leave the building and go to an open space away from damaged areas.
If you are trapped, do not move about or kick up dust.
If you have a cell phone with you, use it to call or text for help.
Tap on a pipe or wall or use a whistle, if you have one, so that rescuers can locate you.
Once safe, monitor local news reports via battery operated radio, TV, social media, and cell phone
text alerts for emergency information and instructions.
Check for injuries and provide assistance if you have training. Assist with rescues if you can do so
safely, etc.
4.1.8 Checking my progress
1. What do you understand by the term Earthquake?
2. Outline the impact do earthquakes human activities and infrastructure?
3. How nuclear weapons testing cause earthquakes?
4. What can you do when you are inside a house during ground shaking?
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4.2. LANDSLIDES.
Activity 4.3: Description of landslides
Fig.4.6: illustration of landslide and the impact on environment.
Observe carefully the above figure and answer the following questions.
a) What do you think could have happened to the area shown in the above figure?
b) Can you think of the major causes this kind situation?
c) Discuss the possible effects of such disaster on human activities and on the environment.
d) Suppose that you are living in a region that is likely to be affected by such disaster, discuss what
would do you to prevent it from occurring. How will you behave if it happens?
4.2.1 Definition of landslide
A landslide, also known as slope movement, mass movement or mass wasting, is the movement by
which soil, sand, and rock move down the slope, typically as a mass, largely under the force of
gravity. It is frequently caused by the soil’s water content which acts as a lubricating agent for failure
to occur.
Fig.4.7: illustration of landslide event with soil, sand and rocks being moved down the slope.
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4.2.2 Causes of landslide
Several factors can increase a slope’s susceptibility to a landslide event. The following are some the
causes:
Water (rainfall or the movement of the sea) this acts as a grease to the material increasing the
likelihood that it will slip and also adds extra weight to the rock
Erosion processes such as coastal erosion and river erosion
Steepness of slope
Rock: soft rock such as mudstone or hard rock such as limestone
Shape of the rock 'grains'
Jointing and orientation of bedding planes
Arrangement of the rock layers
Weathering processes for example freeze-thaw reduces the stickiness (cohesion) between the rock
grains.
Lack of vegetation which would help bind material together
Flooding
Volcanoes and earthquake activity nearby man’s activity mining, traffic vibrations or
urbanization which changes surface water drainage patterns.
4.2.3. Effect of landslides
Due to the movement of rocks, soils, sand mixed with water under the force of gravity, landslides
produce both positive and negative effects:
Among the positive effects we can mention:
Promotion of mining activities.
Building of fertile flood plains for agriculture
Promotion of tourism due to land forms of mass wasting
Promotion of research or study purposes
Soil formation due to the exposure of fresh rocks.
Negative effects
Activity 4.4: Puzzle or cross words.
To do this activity, check the words in the puzzle then after fill it in the missing sentence such that it
will have meaning. It is related to the negative impact of landslide.
E M S A R I D X O R T S
G O V E R N M E N T Y R
O X O R U F X Z W A C K
U W R I D R A I N A G E
D I S P L A C E M E N T
I L R O I S R X U L A G
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Loss of……..
………… of people
………of agriculture, land and crops
Destruction of ………..
Alteration of …… ( e.g. damming rivers)
…….of vegetation
Increase in ………. expenditures
………., etc
4.2.4 Safety measures of landslides
Whenever landslide occurs, it damages many things in different area (eg environment, people,
buildings, roads etc. Some actions are required:
Before a landslide
Do not build your house near steep slope, drainage ways or natural erosion.
Ask information to local officials or geologist on vulnerable area to landslides and corrective
measures you can take if necessary.
Make an evacuation plans for your area how you will communicate with other people.etc
During landslide
Stay alert and awake. Many debris-flow fatalities occur when people are sleeping. Be aware that
intense, short bursts of rain may be particularly dangerous, especially after longer periods of
heavy rainfall and damp weather.
If you are in areas susceptible to landslides and debris flows, remember that driving during an
intensive storm can be dangerous.
Listen for any unusual sounds that might designate moving debris, this can flow quickly and
sometimes without warning that precede a large landslide.
When you are near a steam or channel of water flow, be aware if it increase or decrease, such
changes may indicate landslide activity upstream, so be prepared to move quickly.
Inform affected neighbors. Your neighbors may not be aware of potential hazards. Advising them
of a potential threat may help save lives. Help neighbors who may need assistance to evacuate. Etc
C M E P V T E C I D V R
V A Y R E R K E R I T U
T D O D S U R G T S E O
L O S S U T E U E E R H
M U G E R U M P R A K T
N J U I G R T S O S D K
S H K X A E F L X E S P
E N I F T S I G D S A V
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After landslide
Report quickly the potential hazards as possible for prevention of further hazard and injury.
Look for and report broken utility lines and damaged roadways and railways to the authorities
Search advice for geologist/geotechnical expert for evaluating and best ways to prevent or reduce
landslide risk, without creating further hazard
Look around and check whether the building foundation, chimney, and surrounding land have
damaged.
Help your neighbor who may require individual support, aged people and people with disabilities,
because they may require additional assistance. The same as people who care for them or who
have large families may need a special assistance in emergency situations.
4.2.5 Checking my progress
1. Copy the table into your exercise books and fill it in with the sentences below.
Man’s activity mining brought traffic vibrations which changes surface water drainage patterns.
Ground deformation due to the fact that rocks and debris are swapped by water.
Plant the ground cover on slopes and build retaining walls.
Earthquakes create stresses that make weak slopes fail.
Rainfall or the movement of the sea.
Listen to local radio or television stations for the latest emergency information.
Erosion.
Causes Consequences Preventions
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4.3. TSUNAMI
Activity 4.5: Tsunami event
Fig.4.8: illustration of the devastating effects of Tsunami.
The above figures shows scenarios that where observed during and after a Tsunami had affected a
certain region. Study the picture above carefly these pictures and answer the following questions.
i) What are the main observations?
ii) What do you think could have caused such situations?
iii) From your analysis, to what extent this natural disaster affects human activities and environment?
iv) Imagine your family in such situations as shown above, which advice would you provide to
them?
4.3.1 Definition of Tsunami.
A sudden offset changes the elevation of the ocean and initiates a water wave that travels outward
from the region of sea-floor disruption. Such water waves are called Tsunamis waves and can travel
long distances across the ocean. As an example, large earthquakes in Alaska or Chile have generated
waves that caused damage and deaths in regions as far away as California, Hawaii and Japan.
The world tsunami comes from two Japanese words: Tsu mean “Harbor” and Nami means “wave”
so Tsunami mean a “Harbor wave”. A tsunami is a series of waves in a water body caused by the
displacement of a large volume of water, generally in large lake, volcanic eruptions and other
underwater explosions, landslide, and other disturbances above and below all have a potential to
generate a tsunami.
Generally a tsunami consists of a series of waves with periods ranging from minutes to hours, a small
amplitude (wave height) offshore, and a very long wavelength hundreds of kilometers long, whereas
in normal ocean waves have a wavelength of only 30 or 40 meters. This is why they generally pass
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unnoticed at sea, as they form only a slight swell usually about 300 mm above the normal sea
surface. They grow in height when they reach shallower water.
Tsunamis are sometime referred to as tidal waves. This once popular term from the most common
appearance of tsunami which is that of an extraordinarily high tidal bore, both produce waves of
water that move internal (inland) but in the case of tsunami the inland movement of water may be
much greater, the impression of an exceedingly high and forceful tide. In recent years, the term “tidal
wave” has fallen out of favour, especially in the scientific community, because tsunamis have
nothing to do with tides which are produced by the gravitational pull of the moon and sun rather than
the displacement of water finally tidal wave is discouraged by oceanographers and geologists
Fig.4. 9: illustration of how Tsunami waves increase in amplitude as they approach the shore.
In deep water tsunamis are not large and pose no danger. They are very broad with horizontal
wavelengths of hundreds of kilometers and surface heights much smaller, about one meter. Tsunamis
pose no threat in the deep ocean because they are only a meter or so high in deep water. But as the
wave approaches the shore and the water shallows, all the energy that was distributed throughout the
ocean depth becomes concentrated in the shallow water and the wave height increases, its
wavelength diminishes and its amplitude grows enormously.
Development of Tsunami
Everybody knows that what goes up must come down. This is particularly true for water which
always forms a nice flat surface. So once a disturbance has risen up an amount of water the next step
is for the sea to level itself out and bring it back down. This pushes the water that was underneath it
to spread outwards and thus creating a wave. As this wave travels through the ocean it may
eventually reach the shore. As the sea becomes shallower close to the shore, the energy carried in the
water wave remains unchanged. It compresses the small amount water upwards resulting in
Tsunamis. The stages of process of the development of tsunami are shown on the figure 4.9. The
numbers on the figure correspond to the stage number.
Stage 1: As one plate subducts below another the pressure builds up progressively. After many years
this will result in a section of the megatrust giving way.
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Stage 2: As the section gives way it ruptures the ocean floor causing a massive displacement of
water.
Stage 3: stage 2 can develop due to an earthquake that create a landslide under the sea floor which in
turn would have generated a swell
Stage 4: A Tsunami wave is barely noticeable as a ripple of water near the epicenter
Stage 5: As the wave reaches the cost and the water becomes shallower the size of the wave
increases drastically.
Fig.4. 10: Different stage of Tsunami development process
4.3.2 Causes of Tsunami
The principal cause of tsunami is the displacement of a substantial volume of water or perturbation
of the sea, this displacement of water is usually attributed to either Earthquake, landslide, volcanic
eruption, etc. The waves formed in this way are sustained by full of gravity.
The rapid displacement of water for a large volume, as energy transfers to the water at a rate faster
than the water can be absorbed, the wave did not travel far as it strike land immediately and generate
the landslide. The people fishing in the bay were killed, and another board managed to ride the wave
Volcanoes cause tsunami when there is an eruption. The volcano can either be on land or under the
sea, in which case it is known as a submarine volcano. Violent volcanic eruptions represent also
impulsive disturbances, which can displace a great volume of water and generate extremely
destructive tsunami waves in the immediate source area. The water in the sea then breaks into waves
which travel across the ocean until they come into contact with a coast. Here, a tsunami is formed.
4.3.3 Effects of Tsunami
They are many effect of Tsunami most of them are:
Loss of lives
Death of marine life( aquatic animals)
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Famine
Coastal erosion (the wearing a way of coastal land or beaches)
Structural damage through destruction of people’s properties.
Higher risks of diseases( eg Malaria)
Severe flooding
Displacement of people
Trauma (Psychological effects.)
Government expenditure, etc.
4.3.4 Prevention of tsunami
Unfortunately nothing can be done to prevent Tsunamis. However, there are several organisations
that use complex technology to monitor movement of the earth’s plates and sudden changes in water
movement. There are also warning and evacuation procedures in place around countries with higher
risks like Japan and Hawaii where Tsunamis are frequent.
Any sudden earthquake that happens underwater will be detected in the same manner of an on-shore
earthquake. These are recorded on the Richter scale and depending on its magnitude then warning
systems can be activated to evacuate people.
4.3.5 Checking my progress.
Matching column I with column II
Column I Column II
1. Tsunamis cause damage
by two mechanisms
A. Indicate that the energy of the explosion does not easily generate the
kind of deep, all ocean waveform. Most of energy creates steam and
compression waveforms.
2. Tidal waves B. The smashing force of a wall of water travelling at high speed, and
the destructive power of a large volume of water draining off the land
and transport a large amount of debris or fragment with it, even with
waves that do not appear to be large.
3. The analysis of the
effect of tsunami
C. displacement of volume of water or perturbation of the sea usually
attributed to either Earthquake, landslide, volcanic eruption, etc
4. Impacts of tsunami D. a series of waves in a water body caused by the displacement of a
large volume of water with a very long wavelength hundreds of
kilometers.
5. causes E. are produced by the gravitational pull of the moon and sun rather
than the displacement of water.
6. Tsunami’s definition F. Unfortunately the end products of this are: displacement of people,
structural damage through destruction of people’s properties.
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4.4. FLOODS.
4.4.1 concept of flood
Activity 4.6:
Fig.4.11: Illustration of the impact of floods on human activities and on environments.
a) Critically, analyze the pictures shown in the figure above and write down what is happening.
b) What technical term that describes the scenario. Define the term you have mentioned
c) What are the end results after the occurrence of the disaster shown in the figure above?.
d) Suppose that you are living in the area that is always affected by the disaster, what you would do
to prevent it from occurring again?
Many of us try to generate the process of water cycle in dairy life and rains falling around our
environment cause too much water around our house. People think of what they can do during
rainfall.
Flooding occurs mostly from heavy rainfall when natural watercourses do not have the capacity to
convey excess water. However, floods are not always caused by heavy rainfall.
Fig.4.12: Heavy rain can cause flooding in some areas
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4.4.2 Types of floods
There are three major types flood: Flash floods, rapid on-set floods and slow on-set floods:
(a) Flash floods
This type of flood occurs within a very short time (2-6 hours, and sometimes within minutes) and is usually a
result of heavy rain, dam break or snow melt. Sometimes, intense rainfall from slow moving thunderstorms
can cause it. Flash floods are the most destructive and can be fatal, as people are usually taken by surprise.
There is usually no warning, no preparation and the impact can be very swift and devastating.
(b) Rapid on-set floods
Similar to flash floods, this type of flood takes slightly longer to develop and the flood can last for a day or
two only. It is also very destructive, but does not usually surprise people like flash floods. With rapid on-set
floods, people can quickly put a few things right and escape before it gets very bad.
(c) Slow on-set floods
This kind of flood is usually a result of water bodies over flooding their banks. They tend to develop
slowly and can last for days and weeks. They usually spread over many kilometers and occur more in
flood plains (fields prone to floods in low-lying areas). The effect of this kind of floods on people is
more likely to be due to disease, malnutrition or snakebites.
4.4.3 Causes of floods
Here are a few events that can cause flooding:
Rains: Each time there are more rains than the drainage system can take, there can be floods.
Sometimes, there is heavy rain for a very short period that results in floods. In other times, there may
be light rain for many days and weeks and can also result in floods.
River overflow: Rivers can overflow their banks to cause flooding. This happens when there is more
water upstream than usual, and as it flows downstream to the adjacent low-lying areas (also called a
floodplain), there is a burst and water gets into the land.
Strong winds in coastal areas: Sea water can be carried by massive winds and hurricanes onto dry
coastal lands and cause flooding. Sometimes water from the sea resulting from a tsunami can flow
inland and cause damages.
Dam breaking: Dams are man-made blocks mounted to hold water flowing down from a highland
and this water can be used to generate electricity. Sometimes, too much water held up in the dam can
cause it to break and overflow the area. Excess water can also be intentionally released from the dam
to prevent it from breaking and that can also cause floods.
Ice and snow-melts: In many cold regions, heavy snow over the winter usually stays un-melted for
some time. There are also mountains that have ice on top of them. Sometimes the ice suddenly melts
when the temperature rises, resulting in massive movement of water into places that are usually dry.
This is usually called a snowmelt flood.
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4.4.4 Consequences of floods
Floods can have devastating consequences and can have serious impact on the country’s economy,
the environment, people and animals
a. Economic
During floods, especially flash floods, roads, bridges, farms, houses and automobiles are destroyed.
All these come at a heavy cost to people and the government. It usually takes years for affected
communities to rebuild and business to come back to normalcy.
b. Environment
The environment also suffers when floods happen. Chemicals and other hazardous substances end up
in the water and eventually contaminate the water bodies that floods. Additionally, flooding kills
animals and others insects in the affected areas, distorting the natural balance of the ecosystem.
c. People and animals
Many people and animals may get killed during flash floods. Many more are injured and others
made homeless. Water supply and electricity are disrupted. In addition to this, flooding brings a lot
of diseases and infections and sometimes insects and snakes make their ways to the area and cause a
lot of havoc.
However, there is also something good about floods, especially those that occur in floodplains and
farm fields. Flood water carries lots of nutrients that are deposited in the plains. Farmers love such
soils, as they are perfect for cultivating any kinds of crops.
4.4.5 Floods and safety measures
Sometimes there is no warning of flash floods, and that is why it is important to think of them and
prepare for them before they happen. Here are a few things you can do.
Before the floods
Know about your local relief centers and evacuation routes.
Keep emergency numbers and important information handy, as well as emergency supplies, kits,
first aid items. These may include water, canned food; can opener, battery-operated radio,
flashlight and protective clothing.
Fold and roll up anything onto higher ground (or upper floors of your home), including
chemicals and medicines.
Make sure everything that is of importance is secured (jewelry, documents, pets, and other
valuables).
Plant trees and shrubs and keep a lot of vegetation in your compound if you are in a low-lying
area as that can control erosion and help soften the speed of the flowing water.
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During the floods
Flash floods occur in a short spate of time. As soon as they start, be quick, keep safe and ensure
that children and elderly are safe by leaving the house to a higher ground.
Turn off all electrical appliances, gas, heating and the like if there is a bit of time.
Leave the area before it gets too late. Do not drive through the water as moving water can sweep
you away.
Stay away from power lines or broken power transmission cables.
Try to keep away from flood water as it may contain chemicals or other hazardous materials.
Don't walk, swim or drive through floodwater. Just six inches of fast-flowing water can knock
you over and two feet will float a car.
After the floods
Make sure you have permission from emergency officers to get back inside your house.
Keep all power and electrical appliance off until the house is cleaned up properly and electrical
personnel has confirmed that it is OK to put them on.
Make sure you have photographs, or a record of all the damage, as it may be needed for
insurance claims.
Clean the entire home, together with all the objects in it very well before you use them again.
They may be contaminated.
Keep children and pets away from hazardous sites and floodwater.
Let friends and family know you’re safe. Register yourself as safe on the Safe and Well website.
4.4.6 Checking my progress.
1. Explain how the flood is formed?
2. Draw diagrams showing
i) Infrastructures affected by floods
ii) People trying to save their lives by clinging on a security line to cross a flooded road.
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4.5. CYCLONES AND ANTICYCLONES
Activity 4.8: focused on cyclone
Fig.4.14: illustration of a cyclone and an anticyclone.
Describe the above figure and then after answer the following question:
a) Which direction does the winds moves?
b) Relate hemispheres with these winds.
c) Describe the characteristics of each and their corresponding whether
d) Imagine that such kind of wind comes at certain area/ region, what impact does it have to the area?
Cyclones can be the most intense storms on Earth. A cyclone is a system of winds rotating
counterclockwise in the Northern Hemisphere around a low pressure center. The swirling air rises
and cools, creating clouds and precipitation. Low pressure systems are also known as depressions.
These are systems of air masses forming an oval or circular shape, where pressure is low in the
center and increases towards the periphery.
Fig.4.15: Illustration of the cyclone formation
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4.5.1 Types of cyclones
There are two types of cyclones: Temperate cyclones or depressions and Tropical cyclones.
A. Temperate cyclones or depressions
They rise in the belt of westerly winds and are caused by the mixing of cold air from the Polar
Regions with warm and humid air from tropical regions.
They are dominantly located in temperate regions between 40- 60 degrees North and South of the
equator. The temperate cyclone is also known as middle latitude (mid-latitude)cyclones
e.g. North West Europe, British Columbia, Alaska and the coasts of Chile.
Characteristics of temperate depressions
1. Lowest pressure is near the center of the depression
2. Highest pressure is at the periphery of the system
3. Air circulate around the point of low pressure
4. The circulation is clockwise in the southern hemisphere
5. And anti-clock wise in the northern hemisphere
6. Winds blow towards the center, which is a zone of low pressure
7. They develop over sea or ocean water
8. They affect small area which may not reach 150 km off the coast
9. It is a cyclic form of circulation capable of movement, growth and decay.
Weather associated with temperate cyclones or depressions
It causes rainfall which begins as light showers and progressively become heavier as the warm
front passes
The winds blow in easterly or southeasterly direction
Much of precipitation starts to fall as snow
With the passage of the warm front and arrival of the warm sector, rain ceases apart from
drizzles, temperatures rise and stable stratiform clouds prevail.
Advection fog is common in winter and reduces visibility.
B. Tropical cyclones/ tropical depressions
It is a large scale storm with heavy rainfall and winds which rotate anti-clock wise in the northern
hemisphere and clockwise in the southern hemisphere around and towards a low pressure
atmospheric pressure center.
Characteristics of Tropical cyclones/ tropical depressions
They are among the most destructive storms on the earth’s surface.
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They are given name where they occur and affect a small area.
They develop on either side of equator between 10 and 20 degrees of latitude rarely between if
ever between 5 degrees N and S of the equator.
They originate over sea and oceans water surfaces never over land surfaces
They mainly occur over the western regions of the oceans with a speed of 120km/h
winds which rotate anti-clock wise in the northern hemisphere and clockwise in the southern
hemisphere
In northern hemisphere they are most active in August and early September
While in southern hemisphere they are most active in February and March
4.5.2 Effect of Cyclone
Depending on the location in the world, cyclone takes different name depending on where they
develop so their effects are varied according to the locations.
Name of the
cyclone
Location of the
cyclone
Effects and features
Typhoons Philippine, Japan
and China
Very violent.
Speed of more than 160km/ h
They cause great menace and damages to ships and
building in coastal areas.
Torrential rains, lightning and thunder accompany them.
Tornadoes America,
Caribbean,
Mexico, etc
They are spiral as funnel cloud.
Air swirls rapidly about vertical axis.
Speed between 120 and 500km/h.
they devastate everything in their passage(sweep
house from their foundation, schools, buses, etc)
Destroy bricks buildings.
Counter clockwise in North hemisphere and
clockwise in South Hemisphere.
Hurricanes(e.g:
Katrina)
America,
Caribbean,
Mexico, etc
Named after hurricane and Caribbean god of evil.
Very violent cyclone from tropical latitudes.
Speed between 119 and 250km/h.
They do not form at equator due to limited coriolis
force. Table 4.2: The effects, names and location of cyclone.
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4.5.3 Safety and emergency measures of cyclones.
Activity 4.9: Safety and emergency measures of cyclones.
A girl who wants tour outside countries had to first think of a safe country to visit as she was to stay
there for a couple of weeks. She decides to buy a newspaper from a certain shop (as shown in the fig
above) in order to find the necessary information related to the region where she wanted to go. Inside
the newspaper there was information related to cyclones in that region she had decided to go to and
how people protect themselves against the effects of cyclones.
What do you think were the guidelines in the newspaper on how to conduct herself in case a cyclone
happens when she is in that country?
Before Cyclone
Check whether your home has been built to cyclone standards.
Keep a list of emergency phone numbers on display
Be sure trees around your home are well trimmed.
If you are living away from the floodplain, make plans to secure your property.
Check that the walls, roof and eaves of your home are secured.
Ensure that there is no possibly cause injury or damage during extreme winds.
During the cyclone
Leave the center if it is possible to move.
If you are unable to quit, go to your safe room.
Close all interiors doors and support exterior doors.
lie on the floor under a table or another powerful object.
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After the cyclone
If you are inside the room, don't go outside until officially advised it is safe.
Don't use electric appliances if wet.
Listen to local radio for official warnings and advice.
Be careful of damaged power lines, bridges, buildings, trees, etc.
4.5.4 Anticyclone
Activity 4.10: Description of anticyclone
a) What do you understand by the term “anticyclone”?
b) Categorize the types of anticyclone and explain them.
c) Compare and contrast cyclones and anticyclones. You can even use illustrations to clarify your
answers.
d) Ask your friend whether he/she has ever experienced this disaster in their place? Let him him/her
support his/her answer.
An anticyclone is the opposite of a cyclone. An anticyclone’s winds rotate clockwise in the Northern
Hemisphere around a center of high pressure. Air comes in from above and sinks to the ground. High
pressure centers generally are associated with fair weather
Fig.4. 16: illustration of an anticyclone development
4.5.5 Types of anticyclones
a. Cold anticyclones: are relatively shallow features related to the surface chill(coldness) of the
polar regions
b. Warm anticyclones: they are characterized by cold dense air in the lower troposphere with
relatively warm air above.
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Characteristics of anticyclones
Winds blow from the center to the periphery
Many move slowly and remain stationary for a long time before fading out.
They move northwards
They affect large area( larger than cyclones).
etc
Weather associated with anticyclones
High pressure systems bring clear skies.
Winds are usually light, and blow out of the high pressure area.
Some few clouds giving rise to little rain and drizzle.
High pressure in winter gives us light clouds or clear skies, very low temperatures, calm or light
winds.
etc.
Difference of characteristics between a cyclone and anticyclone
CYCLONES ANTICYCLONES
Pressure decrease toward the centre Pressure increase toward the centre
Violent weather system Calm weather and soft winds
Violent convergence of winds hence heavy
rainfall with thunderstorms
Gentle diverging winds resulting into dry and hot
climates
Form with in the tropics Form outside the tropics
High temperature and high humidity Subsiding air with low humidity and low
temperature
Anticlockwise in the Northern Hemisphere Anticlockwise in the southern Hemisphere
Clockwise in southern Hemisphere Clockwise in Northern Hemisphere
Cover a short area Cover a large area
Take a short time Take a large time
Very fast movement Slow movement
Develop within water where there is no friction Can develop on land Table 4.3: Difference between cyclone and anticyclone
4.5.6 Checking my progress
1. Explain the cause of cyclone.
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4.6 END UNIT ASSESSMENT
4.6.1 Multiple choices.
1. What will happen when the pressure keeps on increasing and the temperature gets higher inside
the ground?
A. the volume decreases and heat energy decreases
B. the volume increases and heat energy decreases
C. the volume increases and heat energy increases
D. the volume and heat energy remain constant.
2. The intensity of an earthquake is measured with a
A. Barometer C. Hydrometer
B. Polygraph D. Seismograph
3. Richter scale is used to measure
A. Temperature of bodies C. Intensity of wind
B. Magnitude of earthquake D. Intensity of earthquake
4.6.2 Structured Questions
1. Copy and complete the sentence below and use your prior knowledge to fill in.
A. Calm weather and soft winds is associated with….….
B. the main difference between a cyclone and an anticyclone is that cyclone has a ………… and
anticyclone has ………….
C. The winds blow from the center to the periphery. This is the …………. of anticyclone
2. Distinguish landslide to the erosion.
3. Why, during earthquakes, tall building and small building are shaken differently? Explain your
answer.
4. Discuss the impact of floods on human activities and suggest ways of minimizing their negative
impact?
5. Explain how floods develop.
6. Why does the earth shake when there is an earthquake?
4.6.3 Essay type questions
1. Explain how erosion, earthquakes and water increase the possibility of landslide to occur?
2. Volcanic activity is one of the causes of the earthquake. What people can do in order to prevent it?
3. Elaborate more on the role of water in landslide.
124
4. Describe different ways of reducing the impact of landslides
UNIT 5. ATOMIC NUCLEI AND RADIOACTIVE DECAY
Fig.5. 1: Sign of radiation precaution.
Key unit Competence
By the end of the unit, I should be able to analyze atomic nuclei and radioactivity decay
My goals
Define atomic mass and atomic number
Identify the constituents of a nucleus
Explain Einstein’s mass-energy relation
Define nuclear fusion and fission
Analyze determinations of a mass of nuclei by using Bainbridge mass spectrometer
Derive the relationship between decay constant and half-life
Determine the stability of a nuclei
Describe properties of different radiations.
Describe creation of artificial isotopes.
Identify the application of radioactivity in life.
Plot a graph of binding energy against nucleon and explain its features.
Calculate the decay rate of unstable isotopes.
Appreciate the safety precautions to be taken when handling radioactive materials.
Appreciate that the nucleus of an atom and quantum system has discrete energy levels.
INTRODUCTORY ACTIVITY: The uses of radiation
125
In different places like industries, hospitals, and other sensitive places, there are different posts that
caution someone about dangerous substances one may encounter if care is not taken. Among the
reasons why these places bare such instruction is because of chemicals and radiations that are used in
such places which may be harmful if not handled with care.
1. Discuss some of the safety signs you have ever seen in any hospitals or industry if you have ever
visited one.
2. Why do you think there is a need to put those signs in such places?
3. It is believed that there are some of diseases that are treated using radioactive substances. Can
you state some of the radiations used to treat some diseases.
4. There are natural men made radioactive substances. All of these are used for different purposes.
What are some of negative effects of these radiations to (i) man , (ii) environment
5. Some countries like Iran are affected by these radiations. Imagine you were a resident of that
country, what would you do to protect yourself from such effects of radioactive substances.
126
5.1 ATOMIC NUCLEI-NUCLIDE
5.1.1 Standard representation of the atomic nucleus
Activity 5.1: Investigating the stable and unstable nucleus
Fig.5. 2 The standard representation of an atom nucleus
Observe the Fig.5.1 above of an atom and answer to the questions that follow:
1. What do numbers A and Z stand for?
2. Describe the relation between the two numbers and their meanings.
3. When do we say that an atom is stable or unstable?
4. Explain clearly the meaning of isotopes. Give an example of isotopes you know.
A nucleus is composed of two types of particles: protons and neutrons. The only exception is the
ordinary hydrogen nucleus, which is a single proton. We describe the atomic nucleus by the number
of protons and neutrons it contains, using the following quantities:
The atomic number or the number of protons Z in the nucleus (sometimes called the charge
number).
The neutron number or the number of neutrons N in the nucleus.
The mass number or the number of nucleons in the nucleus,
A = Z + N. (5.01)
In representing nuclei, it is convenient to use the symbol to show how many protons and
neutrons are present in the nucleus. X represents the chemical symbol of the element. For example,
nucleus has mass number 56 and atomic number 26. It therefore, contains 26 protons and 30
neutrons. When no confusion is likely to arise, we omit the subscript Z because the chemical symbol
can always be used to determine Z. Therefore, is the same as and can also be expressed
as “iron-56.” Each type of atom that contains a unique combination of protons and neutrons is called
nuclide.
5.1.2 Classification
Depending on the combinations of protons and neutrons in the nucleus, nuclides can be classified in
the following 3 categories:
a) Isotopes: These are nuclei of a particular element that contain the same number of protons but
different numbers of neutrons. Most elements have a few stable isotopes and several unstable,
radioactive isotopes.
XA
Z
Fe56
26
Fe56
26 Fe56
127
Example of isotopes:
Oxygen has three stable isotopes that can be found in nature: OO 1716 , and O18
Hydrogen has two stable isotopes H1, H2 and a single radioactive isotope H3 .
Carbon has two stable isotopes 𝐶 614 𝑎𝑛𝑑 𝐶6
12 .
Chlorine has two stable isotopes 𝐶𝑙1735 𝑎𝑛𝑑 𝐶𝑙17
37
Therefore, the chemical properties of different isotopes of an element are identical but they will often
have great differences in nuclear stability. For stable isotopes of light elements, the number of
protons will be almost equal to the number of neutrons. Physical properties of different isotopes of
the same element are different and therefore they cannot be separated by chemical methods i.e. only
physics methods such as the centrifugation method can be used to separate different isotopes of an
element.
b) Isobars: these are nuclei which have the same mass number but different number of protons Z or
neutrons N.
Example of isobars: N14
7and C14
6 which all have 14 as a mass number
c) Isotones: these are nuclei in which the number of neutrons is the same but the mass number A and
the atomic number Z differ
Example of isotones: ,16
8O N15
7and C14
6which all have 8 neutrons.
5.1.3 Units and dimensions in nuclear physics
The standard SI units used to measure length, mass, energy etc. are too large to use conveniently on
an atomic scale. Instead appropriate units are chosen.
The length: The unit of length in nuclear physics is the femtometer.
mfm 15101
This unit is called Fermi in the honor of the Italian Americano physicists who did a lot of pioneering
work in nuclear physics.
The mass: The unit used to measure the mass of an atom is called the atomic mass unit,
abbreviated “amu or u” and is defined as a the mass of an atom of carbon-12. Since mass in
grams of one carbon-12 atom is its atomic mass (12) divided by Avogadro’s number gives
1u =1g
6.02´1023=1.666´10-24 g .
Nuclear masses can be specified in unified atomic mass units (u).
On this scale:
- a neutral C12
6atom is given the exact value 12.000000 u.
- A neutron then has a measured mass of 1.008665 u,
121
128
- a proton 1.007276 u,
- a neutral hydrogen H1
1 atom (proton plus electron) 1.007825 u
Energy: the SI unit used for energy that is Joule is too large. In nuclear physics the appropriate unit
used for energy is an electron volt (eV). An electron volt (eV) is defined as the energy transferred to
a free electron when it is accelerated trough a potential difference of one volt. This means that
JVCeV 1919 106022.11106022.11
It is also a common practice in nuclear physics to quote the rest mass energy calculated using
2mcE , (5.02)
Since the mass of a proton is ukgmp 007276.11067262.1 27 , then 1 u is equal to
kgu
kguu 27
27
1066054.1)007276.1
1067262.1)(0000.1(0000.1
This is equivalent to energy in MeV of
MeVeVJ
smkgmcE 5.931
/106022.1
)/109979.2)(1066054.1(19
228272
Thus, 227 /5.931106605.11 cMeVkgu
The time: the time involved in nuclear phenomena is of the order of 10-20s to million or billion
years.
Nuclear radius: various types of scattering experiments suggest that nuclei are roughly spherical
and appear to have the same density. The data are summarized in the expression called Fermi model.
3
1
0 Arr
(5.03)
Where mfmr 15
0 102.12.1 and A is the mass number of the nucleus
The assumption of a constant density leads to the estimate of the mass density 317102.2 mkg
which is obtained by considering
r =m
V=Au
4p
3r3
=Au
4p
3r0
3A
=1.u
4p
3r0
3
=1.67´10-27kg
4p
3(1.2´10-15 m)3
= 2.2´1017kg ×m-3
This high density can explain why ordinary particles cannot go through the nucleus as highlighted by
Rutherford experiments. The same density was only observed in neutron stars. The nuclear mass can
be determined using a mass spectrometer.
129
5.1.4 Working principle a mass spectrometer
The figure below highlights the working principle of a typical mass spectrometer used to separate
charges of different masses. It can be used to differentiate isotopes of a certain element.
Fig.5. 3: Bainbridge mass spectrometer
Ions are formed in ionization chamber and accelerated towards the cathode. The beam passes through
the cathode and is focused by the collimating slits S1 and S2. The beam is then passed through a
velocity selector in which electric and magnetic fields are applied perpendicular to each other. The
ion moves in straight line path for which both the forces acting on it are equal
qvBqE (5.04)
The velocity of ion which passes un-deflected through the velocity selector is then given by
B
Ev (5.05)
The ions then reach the vacuum chamber where they are affected by the magnetic field (𝐵’) alone
and then move in circular paths; the lighter ions having the larger path radius. If the mass of an ion is
m, its charge q and its velocity v then
R
mvqvB
2
' (5.06)
Bq
mvR
(5.07)
The radius of the path in the deflection chamber is directly proportional to the mass of the ion. The
detection is done by photographic plate when the ions fall on it. The fig. 5.5 shows the recorded mass
130
spectrum for a gas containing three isotopes. Note the wider line for the mass m1, showing its
relatively greater abundance.
Fig.5. 4: A recorded mass spectrum of a gas containing 3 isotopes
5.1.5 Checking my progress
1. Write down:
A. A word which describes the relations between the following elements 𝐶612 and 𝐶6
14
B. The nuclide symbol for an atom of chlorine (𝐶𝑙) which contains 17 protons and 18 neutrons.
2. Here is a list of particles studied in high school physics: electron, neutron, and proton. From the
list, choose one particle which
A. Has a positive charge
B. Is found in the nucleus of an atom
C. Is uncharged
3. How many electrons and protons are there in the following element 𝑋56143 ? What does the symbol
X means for you?
4. The number of neutrons in a nucleus of gold whose symbol is Au197
79 is:
A. 79 C. 197
B. 118 D. 276
5. Calculate the number of neutrons in the following atoms
A. Al27
13 C. Uns262
107
B. P31
15 D. Os190
76
6. How many neutrons are in an atom of strontium- 90?
7. Use the information given in the table below to answer the questions below concerning the
elements Q, R, S, T and X.
Element Atomic number Mass number Electron structure
Q 3 7 2,1
R 12 24 2,8,2
S 18 40 2,8,8
T 8 18 2,6
X 19 39 2,8,8,1 Table 5. 1 Some elements of a periodic table
131
5.2 MASS DEFECT AND BIDING ENERGY
5.2.1 Mass defect
Activity 5.2 Select the words in the following puzzle.
Observe the puzzle below.
1. Discover 8 different words related to particle Physics hidden in the puzzle below, and write
them in your notebook.
2. Use them to formulate a meaningful sentence
A N I S A K I L O G R A M
X T R U N Q V U L Z I J W
E C W F I F A D S E M A C
J L T O R A N E E Q A S A
K E E R U R Y E A W S D L
E A Q C D J A E F T S U Q
R S H E T H W C G U O W O
W I T M A R I T W O T Q Y
Q F B G E F O A E H W T E
B I D O N G L N T M I U N
A W U D E B O N V L H F E
I Y O P O W I S I O E A R
N U C L E U S B I W L U G
L O P O T Z A W Q Y B T Y
G S D R W T B E L I D O N
D A M W S E I N S T E I N Table 5. 2 Cross word puzzle
3. Complete the sentences below using the words you discovered in the puzzle
a) An …….is the SI unit of energy.
b) On the atomic scale, the ………..is not the SI unit of mass.
c) The ………..of nucleons is greater than the mass of a nucleus.
d) The atom releases ………when its nucleus is formed from its constituent particles
e) The binding energy per nucleon gives an indication of the …………of the nucleus.
f) The surprising suggestion that energy and mass are equivalent was made by ……in 1905.
4. Discuss and explain the meaning of the following expression as used in physics
A. Mass defect C. Electron volt
B. Biding energy D. Stable nuclides
The nucleus is composed of protons that are positively charged and neutrons that are neutral. The
question is what is holding these particles together in this tiny space?
Experiences have demonstrated that the mass of a nucleus as a whole is always less than the sum of
the individual masses of protons and neutrons composing that nucleus.
132
The difference between the two measurements is called mass defect m . For a nucleus XA
Z the
mass defect is given by:
Nnp MmZAmZm )(
(5.08)
Example 5.1: He4
2 mass compared to its constituents
1. Compare the mass of a He4
2 atom to the total mass of its constituent particles.
Answer
The He4
2 nucleus contains 2 protons and 2 neutrons. Periodic tables normally give the masses of
neutral atoms—that is, nucleus plus its Z electrons. We must therefore be sure to balance out the
electrons when we compare masses. Thus we use the mass H1
1 of rather than that of a proton alone.
We look up the mass of the atom in periodic table (it includes the mass of 2 electrons), as well as
the mass for the 2 neutrons and 2 hydrogen atoms (= 2 protons + 2 electrons).
The mass of a neutral He4
2 atom, from periodic table is umHe 002603.4
The mass of two neutrons and two H atoms (2 protons including the 2 electrons is
uumn 017330.2)008665.1(22
uumH 015650.2)007825.1(22
Thus uuumm Hn 032980.4017330.2017330.222
Therefore the mass of He4
2 is measured to be less than the masses of its constituents by an amount
uuummmm Hepn 030377.0002603.4032980.4
5.2.2 Einstein mass-energy relation
In 1905, while developing his special theory of relativity, Einstein made the surprising suggestion
that energy and mass are equivalent. He predicted that if the energy of a body changes by an amount
of energy E, its mass changes by an amount m given by the equation
2mcE (5.02)
Where c is the speed of light and m mass of a body
Everyday examples of energy gain are much too small to produce detectable changes of mass.
133
Example 5.2
1. When 1 kg of water absorbs 4.2 x 103 J to produce a temperature rise of 1K, calculate the
increase in mass of water.
Answer
kgsm
J
c
Em 5
28
3
2104.1
)/103(
102.4
5.2.3 Binding energy
The mass of a nucleus is less than the combined mass of its protons and neutrons (nucleons). The
missing mass is called the mass defect. This observed mass defect represent a certain amount of
energy in the nucleus known as the binding energy 𝐸𝑏and calculated using the Einstein formula as:
2mcE (5.08)
where c is the speed of light and m the mass defect.
The binding energy for a nucleus containing Z protons and N neutrons is defined as
2)( cmNmZmE A
ZnH (5.09)
where
- mA
Zis the mass of the neutral atom containing the nucleus, the quantity in the parentheses is the
mass defect, mNmZmm A
ZnH
- uMeVc /5.9312
The binding energy is the energy released when a nucleus is formed from its constituent particles or
the energy required to break up (to split) the nucleus into protons and neutrons. Protons and electrons
are held together in the nucleus of an atom by the strong nuclear force. So if we imagine splitting a
nucleus up into its separate protons and neutrons, it would require energy, because we would need to
overcome the strong nuclear force.
5.2.4 Binding energy per nucleon and stability
Instead of looking at the total binding energy of a nucleus, it is often more useful to consider the
binding energy per nucleon. This is the total biding energy divided by the total number of nucleons.
A
mc
A
EEb
2
(5.10)
134
Example 5.3: Binding energy
1. Computer the binding energy per nucleon for α particle?
Answer:
Alpha particles are helium nuclei He4
2 and the mass of helium nuclide umaM N 00153.4
u
Mmmm Nnp
03029.000153.4)00866.12()00725.12(
22
MeVcuEb 3.2803029.0 2 And MeVMeV
A
Eb 0725.74
3.28
Since2/494.9311 CMeVamu
The binding energy per nucleon is defined as the total binding energy of the nucleus divide by the
mass number of the nuclide
MeVA
Eb 07.74
3.28
A plot of binding energy per nucleon Eb/A as a function of mass number A for various stable nuclei is
shown on Fig. 5.6.
Fig.5. 5: The graph of binding energy per nucleon of the known elements (Giancoli D. C., 2005)
135
The nuclear binding energy per nucleon for light element increases with the mass number until a
certain maximum is reached at around A = 56 and then after it almost saturate. The fact that there is a
peak in the binding energy per nucleon curve means that either the breaking of heavier nucleus
(fission) or the combination of lighter nuclei (fusion) will yield the product nuclei with greater
binding energy per nucleon and therefore more stable.
As an example if a nucleus like U238
92 is split into two fragments of nearly equal masses, the two
fragments will have higher binding energy per nucleon than the original. The excess energy is
released as useful energy and this process called fission is the basis of electricity production in a
nucleus plant.
If two light elements combine their nuclei in one nucleus, the formed nucleus will have a greater
binding energy per nucleon than the originals.
energyHeHH 4
2
2
1
2
1 (5.11)
This process is called nuclear fusion and can only take place at a very high temperature. It is the
source of energy in the sun and other stars. The fusion is more energetic than the fission.
The binding energy per nucleon therefore gives an indication of the stability of the nucleus. A high
binding energy per nucleon indicates a high degree of stability – it would require a lot of energy to
take these nucleons apart.
5.2.5 Checking my progress
1. (a) What is mass defect?
(b) Why does a mass defect occur?
(c) What is biding energy?
2. When 1.00 kg of water absorbs 4.2 × 103𝐽 of energy to produce a temperature rise of 1 K, what
will be the increase in mass of the water?
3. Consider an example of 𝐻24 which has an atomic mass of 4.0026 u, this includes the mass of its
two electrons. Its constituents comprise two neutrons each of mass 1.0087u and protons each having
a mass of 1.0078 u. Find the total mass of the particles and compute its biding energy.
5. Calculate the biding energy of O16
8 and its biding energy per nucleon. The mass of neutral O16
8 is
15.994915 u.
136
5.3 RADIOACTIVITY AND NUCLEAR STABILITY
Activity 5.3: Investigating radioactivity
During the World War II, its final stage was marked by the atomic bombing on Nagasaki and
Hiroshima towns in Japan (Fig.5.7). Observe the image and read the text provided below before
answering the following questions.
Fig.5. 6: The atomic bomb in Nagasaki (Japan in 1945)
In August 1945, after four years of world war, united States B-29 bomber, dropped the atomic bomb
over the cities of Hiroshima on August 6th 1945. 70.000 people died in 9 seconds, and the city of
Hiroshima was leveled. 3 days after as second bomb was dropped in Nagasaki, Japan with the same
devastating results. The bombing killed over 129.000 people.
The bomb released cataclysmic load of energy. The ones who were close enough to see the blast lost
their eyes. It was the last thing they ever saw. The bright light of what the blinded them. The black of
their eyes, the retina, melted away. The radiation received by the body is equivalent today’s
thousands of x-rays. The human body can’t absorb unlimited radiation. It falls apart because the cells
are dying of radiation poisoning, if the radiation is intense enough, it looks like a urn. Layers of the
skin begin to fall off. The body vital functioning began to slow down until it stops.
1. Describe and discuss the phenomena happening on two images.
2. From the text, show that the atomic bomb of Hiroshima was very harmful to human body.
3. What are the types of radiations should be there?
4. Stable isotopes do not emit radiations. What is the name of materials which emit radiations?
Describe them.
5. What are the possible main radioisotopes used to produce energy in figure above?
6. Which processes are used to generate such heavy energy? Describe any one of your choice
Radioactivity is one of the dynamic properties of nuclei, in this process the system makes a transition
from a high energy state to a low energy by emitting α and β-particles or γ-rays. This process
happens naturally and is not affected by any external agent such as pressure, temperature or electric
and magnetic fields. The α-particles are Helium nuclei and can be stopped by a piece of paper while
β-particles are either electron or positron. There are high energetic particles and can pass through one
cm thick aluminum sheet. γ-rays are electromagnetic radiations and can be stopped by several inches
of lead.
137
5.3.1 Radioactive decay of a single parent
Nucleus decay is a random process and the rate of disintegration is proportional to the number of
available radioactive nuclides. Let us analyses the simple case where the first daughter nuclide is
stable. Suppose that at time t, there are N radioactive nuclide and dN is the number of nuclide
disintegrating within a time dt. As the rate of disintegration is proportional to the number of nuclides
present in the radioactive substance, we get
Ndt
dN , (5.12)
where λ, the proportionality constant, is called the radioactive constant.
This constant depends on the nature of the radioactive substance. The negative sign shows that an
increase in disintegration rate will decrease the number of radioactive nuclides which are present.
From this we can establish the formula of radioactive decay:
teNN 0 , (5.13)
where it assumed that the initial number of radioactive nuclide is equal to N0.
Fig.5. 7: Illustration of the radioactive decay law
If we consider the activity A of a radioactive sample which is the number of decay events in a unit
time we obtain a similar expression for the radioactive decay law but expressed in terms of activity
of the radioactive substance:
teAA 0 , (5.14)
where A0 is the initial activity of the radioactive source.
Another parameter useful in characterizing nuclear decay is the half-life 𝑻𝟏
𝟐
.
138
The half-life of a radioactive substance is the time interval during which half of a given number of
radioactive nuclei decay. Therefore the half time period is
2ln
21 T (5.15)
Finally, one shows that the mean-life of a nuclide or the average life period of a nuclide is related to
the radioactive constant by
1 (5.16)
In general, after n half-lives, the number of un-decayed radioactive nuclei remaining is .
A frequently used unit of activity is the Curie (Ci), defined as .This value
was originally selected because it is the approximate the activity of 1 g of radium.
The SI unit of activity was named after Henry Becquerel (Becquerel: Bq)
Therefore, the curie is a rather large unit, and the more frequently used activity
units are the mill curie and the micro curie.
Example 5.3 Sample activity
1. The isotope C14
6 has a half-life of 5730 yr. If a sample contains
221000.1 carbon -14 nuclei,
what is the activity of the sample?
Answer
The half life time in second sT 74
1
2/1 10156.3573303652436005730
The decay constant 112
2/1
1083.32ln s
T
The activity or rate decay BqsNt
NA 1022112 1083.3)1000.1)(1083.3(
5.3.2 Characteristics of radioactive substances
Radioactive substances (nuclides) present one or more of the following features
nN )2
1(0
sdecaysCi /107.31 10
sdecayBq /11
BqCi 10107.31
139
The atom of radioactive elements are continually decaying into simpler atoms as a result of
emitting radiation
The radiations from radioactive elements produce bright flashes of light when they strike
certain compounds. The compound fluoresce. For example, rays from radium cause zinc
sulphide to give off light in the dark. For this reason, a mixture of radium and zinc sulphide
is used to make luminous paints.
They cause ionization of air molecules. The radiations from radioactive substances knock out
electrons from molecules of air. This leaves the gas molecules with a positive charge.
Radiations from radioactive substances can penetrate the heavy black wrapping around a
photographic film. When the film is developed, it appears black where the radiations struck
the film.
Radiations from radioactive substances can destroy the germinating power of plants seeds,
kill bacteria or burn or kill animals and plants. Radiations can also kill cancers.
a) Properties of emitted radiations
Some of their properties are summarized and shown in the table below:
Radiation Nature Relative
charge
Relative effect
of electric and
magnetic field
Penetration Distance
travelled
through
the air
Effect on
nucleus
Alpha
particle
2 protons
and 2
neutrons
as.
2 Small
deflection
Stopped by a
few sheets of
paper
A few cm A
decreases
by 4 and Z
by 2
Beta
particle
Electrons -1 Large
deflection
Stopped by a
few mm of
plastic
A few m
Gamma
rays
Electroma
gnetic
radiation
0 No deflection Stopped by
several cm of
lead
A few km No change
to mass or
atomic
number but
the nucleus
does lose
energy.
Table 5. 3 Properties of different types of radiations
a) Alpha decay ( 𝑯𝒆)𝟐𝟒
If one element changes into another by alpha decay, the process is called transmutation. For alpha
emission to occur, the mass of the parent must be greater than the combined mass of the daughter and
the alpha particle.
In the decay process, this excess of mass is converted into energy of other forms and appears in the
form of kinetic energy of both the daughter nucleus and the alpha particle. Most of kinetic energy is
140
carried away by the alpha particle because it is much less massive than the daughter nucleus. The
momentum is conserved in this process.
The isotope whose natural radioactive decay involves the emission of alpha particles usually have a
relative atomic mass greater than 210 (Ar>210). They have too much mass to be stable and give out
alpha particles to form smaller and more stable atoms.
Example 1: Radium 226 (Ra) decays with the emission of an α-particle to form an inert gas radon
(Rn) ( 𝑅𝑛)86222 .
The transformation is given by 𝑋 → 𝑌 +𝑍−2𝐴−4
𝑍𝐴 𝐻𝑒2
4
Example 2: 𝑅𝑎88226 − 𝐻𝑒2
4 = 𝑅𝑛86222 Or 𝑅𝑎88
226 → 𝐻𝑒24 + 𝑅𝑛86
222 .
where 𝑯𝒆𝟐𝟒 is alpha particle. Both the mass (226 − 4 = 222) and the charge (88 − 2 = 86) must be
conserved.
Radon is also unstable, and decays with the emission of an alpha particle: 𝑅𝑛 − 𝐻𝑒 = 24 𝑃𝑜84
21886
222
Polonium is also an alpha particle emitter 𝑃𝑜 −84218 𝐻𝑒2
4 = 𝑃𝑏82214
b) Beta decay
The isotopes whose radioactive decay involves the emission of beta particles often have a relative
atomic mass less than 210 (Ar < 210). Beta particles are usually emitted from heavier nuclei that have
too many neutrons compared with the number of protons
i. Negative β-decay
In this process of negative β-decay an electron and an antineutrino are emitted.
eYX A
Z
A
Z
0
11
1
Examples of negative β emitters are given below
114
7
14
6
132
16
32
15
NC
SP
𝑇ℎ81208 → 𝑃𝑏82
208 + 𝛽−10 + �̅�
The emitted electron results from the following reaction where a neutron changes into a proton and
an electron is emitted from the nucleus as a beta particle:
epn 0
1
1
1
1
0
The conservation of charges and mass number is maintained. The daughter nuclide may be in an
excited state and will become stable after emitting a γ-ray.
141
ii. Positive β-decay
In this process the positron and the neutrino are emitted.
eYX A
Z
A
Z
0
11
This positive decay is different from an electron capture which takes place when an electron that is
close to the nucleus recombines with a proton in the nucleus producing a neutron and a neutrino:
1
1p+-1
0n¾®¾0
1n+n
The equation of decay of the electron capture is:
Z
AX e.c¾ ®¾Z-1
AY
The daughter nuclide is seem to be the same as that we could have been produced if a positron has
been emitted. The rearrangement of the remaining Z-1electrons will lead to emission of characteristic
x-ray of the daughter nucleus. In few case both positron and electron capture may happen.
c) Gamma decay (𝜸)
Very often a nucleus that undergoes radioactive decay is left in an excited energy state. The nucleus
can then undergo a second decay to a lower energy state by emitting one or more photons. Unlike α
and β decay, γ decay results in the production of photons that have zero mass and no electric charge.
The photons, emitted in such process, are called gamma rays and they have very high energy.
If an atom of a material Y emits a γ ray (γ photon), then the nuclear reaction can be represented
symbolically as
𝑌 → 𝑌 +𝑍𝐴
𝑍𝐴 γ.
Gamma emission does not result in any change in either Z or A.
Notes:
- A transmutation does not occur in gamma decay. When an alpha particles and beta particles are
emitted, gamma rays are often emitted at the same time. When a radioisotope emits gamma rays,
it become more stable because it loses energy.
- In both alpha and beta decay, the new element formed is called the daughter isotope.
- Gamma rays are like X-rays. Typical gamma rays are of a higher frequency and thus higher
energy than X-rays.
- Deviations of alpha, beta and gamma radiations due to electric field and magnetic field ( See
Fig.5.9). It can be seen unlike gamma-rays, alpha and 𝛽-particles are affected by the presence of
electric and magnetic fields since these particles are charged. Gamma-rays are not affected by
these fields.
142
Fig.5. 8: Deviation of radiation particles in an electric field
5.3.3 Nuclear fission and Fusion
a) Nuclear fission
Heavy unstable nuclides can be broken up to produce energy in a process called nuclear fission.
When uranium decays naturally, alpha and beta particles are emitted. However, when uranium-235 is
bombarded by neutrons it forms uranium-236. Uranium-236 is unstable and breaks down, splitting
into two large particles and emitting three neutrons. The fission of by thermal neutrons can be
represented by the reaction
𝑛 + 𝑈92235 → 𝑈∗ → 𝑋 + 𝑌 + 𝑛𝑒𝑢𝑡𝑟𝑜𝑛𝑠92
23601 ,
where is an intermediate excited state that lasts for approximately before splitting into
medium-mass nuclei X and Y, and these are called fission fragments.
Example: 𝑈 + 𝑛01 → 𝑈 → 𝐵𝑎56
141 + 𝐾𝑟 +3692 3 𝑛0
192
23692
235
Fig.5. 9: Fission diagram illustration
U235
U236 s1210
143
When the exact masses of the final products are added together, the sum is found to be appreciably
less than the exact masses of the uranium-235 and the original neutron. This difference in mass
appears as energy given by
Another important point arises! The three neutrons released may collide with other nuclides and split
them also resulting in cascade reactions. In this way, chain reactions occur and as a result, the
quantity of energy released can be very large. A few kilogram of uranium can produce as much heat
energy as thousands of tons of coal.
Advantages and disadvantages of nuclear fission
The nuclear fission produces a huge amount of energy. This energy can be released in a controlled
manner in nuclear power station and be used in driving steam turbines that produce electric power.
However, when produced in uncontrolled manner it will result in the fabrication of atomic bomb that
may release a large amount of heat energy and damaging radiations. The emitted radiations have
both short term and long term effect on the living things.
b) Nuclear fusion
When lighter nuclides merge together in a process called fusion, energy is produced and mass is lost.
For example:
𝐻11 + 𝐻1
1 → 𝐻𝑒12 + 𝑒+ + 𝜐
𝐻11 + 𝐻1
2 → 𝐻𝑒23 + 𝛾
These reactions occur in the core of a star and are responsible for the outpouring of energy from the
star.
𝐻𝑒23 + 𝐻𝑒2
3 → 𝐻𝑒24 + 𝐻 + 𝐻1
111
The above 3 reactions can be summarized as:
41
1H¾®¾2
4He+2+1
0e+2g +2n
The sum of the exact masses of the helium atom is less than the sum of exact masses of the four
hydrogen atoms. This lost mass is released as energy. It is thought that the sun’s energy is produced
by nuclear fusion.
5.3.4 Radiation detectors
Activity 5.4: Smoke detector bellow
Observe the diagram of a smoke detector bellow then answer to the questions that follow:
m
2mcE
144
Fig.5. 10: illustration diagram of a smoke detector
1. Name the components labeled A, B, C and D on the smoke detector above?
2. What is meant by smoke detector?
3. Describe a functioning of a smoke detector.
4. Design an inventory of other radiation detectors you know.
Experiments in Nuclear and Particle Physics depend upon the detection of primary radiation/particle
and that of the product particles if any. The detection is made possible by the interaction of nuclear
radiation with atomic electrons directly or indirectly.
a-Classification of radiation detectors
There are a variety of other radioactive detectors that we may conveniently classify into two classes:
Electrical and Optical detectors.
Types Detector
Electric - Ionization Chamber
- Proportional Counter
- Geiger-Müller Counter
- Semi-conductor detector
- Neutron Detector
- Scintillation Counter
- Cerenkov Counter
Optical - Photographic Emulsion
- Expansion Cloud Chamber
- Diffusion Cloud Chamber
- Bubble Chamber
- Spark Chamber
Table5. 1 Classification of radiation detectors
b-Working principle of an ionization chamber
Conventionally, the term "ionization chamber" is used exclusively to describe those detectors
which collect all the charges created by direct ionization within the gas through the
application of an electric field. Ionization chamber is filled with inert gases at low pressure.
145
In the chamber there are two electrodes, namely, the cathode and the anode which are
maintained at a high potential difference as shown on the figure below
Fig,5.11: visualization of ion chamber operation
When radiation enters the chamber, it ionizes the gas atoms creating negative and positive
charges. The negative charges or electrons are attracted by the anode while positive ions are
attracted by the cathode; this produces the current in the outside circuit depending on the
strength and the type of radiation. The current produced is quite small and dc amplified
electrometers are used to measure such small currents.
5.3.5 Checking my progress
In the following exercises (1 to 4), choose the best answer and explain your choice
1. Which of the following is an electron?
A. Neutrino C. Photon
B. Gamma particle D. Beta particle
2. Which of the following most accurately describe radioactive decay?
A. Molecules spontaneously break apart to produce energy
B. Atoms spontaneously break apart to produce energy beta decay, alpha decay and positron
emission are all forms of radioactive decay. Energy is released because the atoms are converted
to a more stable energy
C. Protons and neutrons spontaneously break apart to produce energy
D. Electrons spontaneously break apart to produce energy
3. Which of the following is true concerning the ratio neutrons to protons in stable atoms?
A. The ratio for all stable atoms is 1:1.
B. The ratio for small stable atoms is 1:1, and the ratio for large stable atom is greater than 1:1. As
atomic weight goes up, the ratio of neutrons to protons for stable atoms increases up to as much
as 1.8:1 ratio.
C. The ratio for large stable atom is 1:1, and the ratio for small stable atoms is greater than 1:1.
146
D. There is no correlation between the stability of the atom and its neutron to proton ratio.
4. Polonium-218 undergoes one alpha decay and two beta decays to make
A. Polonium-214 C. Bismuth-214
B. Plomb-214 D. Plomb-210
5. a) Compare (i) the charge possessed by alpha, beta and gamma radiations
(ii) The penetrating power of these radiations
6. a) What is meant by the term (i) radioactive decay? (ii) Half-life of a radioactive substance?
b) A 32 g sample of radioactive material was reduced to 2 g in 96 days. What is its half-life? How
much of it will remain after another 96 days?
7. Bi212 Decays to Th208 by α-emission in 34% of the disintegration and to Ra212 by β-emission in
66% of the disintegration. If the total half value period is 60.5 minutes, find the decay constants
for alpha and beta and the total emission.
8. If a radioactive material initially contains 3.0milligrams of Uranium U234 , how much it will
contain after 150,000 years? What will be its activity at the end of this time? (T=2.50x105 years,
λ= 8.80 x10-14 per second)
147
5.4 APPLICATION OF RADIOACTIVITY
Activity 5.5: Use of nuclear energy to generate electricity
Fig.5. 12: Nuclear power plant functioning mechanism diagram.
Many people disagree to the use of nuclear power to generate our electricity, even though the safety
record of nuclear industry is extremely good. Observe clearly the image diagram of the nuclear
power plant (Fig.5.13) and answer to the questions that follow
1. Why do you think people disagree to the use of nuclear power station?
2. What are the main parts of the power plant station observed in Fig.5.13?
3. Analyze and explain the steps of energy transformation from reactor to generator
4. Write a brief explanation on the advantages and disadvantages of using nuclear energy as a
source of electricity if any.
5. Use internet and your library or any other resources to find out about the other application of
radionuclides in our daily life
People would not have fear of radiations when controlled in certain manner. Radioisotopes and
nuclear power process have been used and produced improvement in various sectors. These includes:
consumer products, food and agriculture, industry, medicine and scientific research, transport, water
resources and the environment. The following are some descriptive examples among others.
5.4.1 Industry
Different materials we use at home are manufactured in industry and made of different radioactive
materials. The dosage of use of radioactive substance is thus controlled so that they are not harmful
to human body.
Gamma radiation and beta radiation from radio-isotopes can be used to monitor the level of the
material inside the container. The penetrating power of gamma rays is used to detect hidden flow in
148
metal castings. Beta rays are used to measure the thickness of various flat objects (the mass absorbed
by the object is proportional to its thickness).
In the textile industries, irradiation with beta radiations fixes various chemicals onto cotton fibers.
This produces for instance permanent press clothing. Again, radioactive materials can be used as
tracers to investigate the flow of liquids in chemical factories.
Fig.5. 13 Testing the level of a liquid in a container using radiations
If there is a sudden decrease in the amount of radiation reaching the detector, which will happen
when the container is full, then this can be used as a signal to switch off the flow of substance into
the container. A similar method is used to monitor the thickness of sheets of plastic, metal and paper
in production
5.4.2 Tracer studies
Tracer techniques can be used to track where substances go to and where leaks may have occurred.
Leaks in gas pipes or oil pipes can be detected by using this technique.
Tracer techniques are also used in medicine to treat thyroid glands which can be underactive or over
active. The activity of the thyroid gland can be monitored by the patient being injected with or asked
to drink radioactive iodine. The radioactivity in the vicinity of the thyroid gland is then checked to
see how much of the radioactive iodine has settled in the area around the gland.
5.4.3 Nuclear power stations
Nuclear power stations control a large amounts of energy released when Uranium-235undergoes
nuclear fission. The energy released by this controlled chain reaction, is then used to produce
electricity.
5.4.4 Nuclear fusion
In nuclear fusion, the nuclei of elements with a very low atomic number are fused together to make
heavier elements. When this takes place, it is accompanied by a very large release of energy. In the
149
sun, hydrogen nuclei are fusing together all the time to make helium nuclei. This is also the process
by which a hydrogen bomb works.
5.4.5 Medicine
Activity 5.6: Radionuclides in Medicine
Observe the figure below and suggest answers to the question below
Fig.5. 14: A gamma camera assembly. The photons emitted in the patients are detected by the photomultiplier
tubes. A computer monitor displays the image computed from the photomultiplier signals.
1. Who is this person (a man or a woman)?
2. Where is he?
3. What does the image on the right represent?
4. What do you think the patient is suffering from?
5. Using the knowledge acquired in optics, what kind of light propagation observed there?
6. Does the imaging use reflection or refraction? Why?
7. What should be the name of radiation being used in this imaging?
Nuclear medicine has revolved treatment of different disease of the century. It consists on the use of
nuclear properties of radioactive substances in diagnosis, therapy and research to evaluate metabolic,
physiologic and pathologic conditions of human body. Today, nuclear medicine is currently used in
the diagnosis, treatment and prevention of many serious sicknesses.
Cancer cells are more easily killed by radiation than healthy cells. In medicine, penetrating gamma
rays of cobalt-60 sources are used for this purpose.
Other cancers such as skin cancers are treated by less penetrating beta radiation from strontium-90
source. Surgical instruments can also be sterilized using gamma radiation
150
5.4.6 Food preservation
The preservation of food uses gamma rays is spreading worldwide. Treating food with gamma rays
can:
Slow down the ripening of some fruits and the sprouting of potatoes. In both cases, this helps
storage and increases the half-life of the food.
Kill highly dangerous micro-organisms such as salmonella
Kill micro-organisms that spoil food
5.4.7 Radiocarbon dating
There are three isotopes of carbon: carbon-12, carbon-13 and carbon-14. The isotope carbon-14 is
radioactive and has half-life of 5760 years. To estimate the age of a biological sample, radiocarbon
C14
6 is used as a radioactive nuclide.
Nucleus decay is independent of the physical or chemical condition imposed on the elements. This
can be used to measure the ages of biological samples by considering the ratio of C14
6 which is
radioactive and C12
6 in dead species. Radioactive carbon is produced when cosmic rays interact with
air atoms to produce neutrons and these neutrons interact with nitrogen
HCnN 1
1
14
6
1
0
14
7
The half-life period of C14
6 is equal to 5760 years. The carbon reacts with oxygen to produce CO2
and plants combine this CO2 with water in the process of photosynthesis to manufacture their food.
Therefore plants and animals are radioactive. When plants or animals die, the C14
6 in them keeps on
decaying without any new intake. The ratio of C14
6 and C12
6 will therefore be different in dead and
leaving plants and animals. The age of the dead plant or animal can be estimated by measuring this
ratio.
Radioactive
substance
Material tested Half-life
(years)
Potential range
(years)
Carbon 14 Wood, charcoal, shell 5730 70000
Protactinium 231 Deep sea sediment 32000 120000
Thorium 230 Deep sea sediment, coral shell 75000 400000
Uranium 234 Coral 250000 1000000
Chlorine 36 Igneous and volcanic rocks 3000000 500000
Beryllium 10 Deep sea sediment 2.5 billion 800000
Helium 4 Coral shell 4.5 billion -
Potassium 40 Volcanic ash (containing decay product
of argon 40)
1.3 billion -
Table 5. 4 Half-life of some radioactive substances
151
5.4.8 Agricultural uses
In agriculture, radionuclides are used as tracers for studying plants, insect and animals. For example,
phosphorus-32 can be added to plant fertilizer. Phosphorus is absorbed by plants and its distribution
can be measured.
Radiation has been used in South American to detect and control the screw worm fly pest. A large
number of the male of the species were exposed to gamma radiation. When the males were released
back into the wild and mated with wild females, sterile eggs resulted and no new flies were born.
The points of photosynthesis in a leaf are revealed by growing it in air containing carbon-14. The
presence of this radioactive nuclide in the leaf is the revealed by putting the leaf onto a photographic
plate and letting it take its own picture.
5.4.9 Checking my progress
1. Suggest different uses of radionuclides in (i) Medicine (ii) food and agriculture
2. In our daily life, we are exposed to radiations of different types mainly in materials we use.
a) Make an inventory of all of the devices in your home that may have (contain) a radioactive
substance.
b) What is the origin of these radiations in the materials highlighted above?
c) Explain the purpose of radioactive material in the device.
d) Then make research to find out how the objects shown inFig.5.15 use radiation in their
manufacture.
Fig.5. 15
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5.5 HAZARDS AND SAFETY PRECAUTIONS OF WHEN HANDLING
RADIATIONS
Activity 5.8: Investigating the safety in a place with radiations
Fig.5. 16: Radiation effects on human body according to the exposure.
The image above (Fig.5.16) shows different side effects of radiation on human body according to the
exposure time taken. With reference to section 5.3 and activity 5.3, answer to the following
questions:
1. What are the dangers of radiations you may observe?
2. Analyze measures should be taken for radiation users?
5.5.1 Dangers of radioactivity
Both beta particles and gamma rays can pass easily in the skin and can easily destroy or even kill
cells, causing illness.
They can cause mutations in a cell’s DNA, which means that it cannot reproduce properly, which
may lead to diseases such as cancer.
Alpha particles cannot pass through the skin. However, they are extremely dangerous when they
get inside your body. This can happen if you inhale radioactive material.
5.5.2 Safety precautions when Handling Radiations
The precautions taken by workers who deal with radioactive materials are:
Wearing protective suits
Wearing radiation level badges
153
Checking the radiation level regularly
Using thick lead-walled containers for transporting radioactive materials
Using remote control equipment from behind thick glass or lead walls to handle radioactive
material
They should be held with forceps and never touched with hands.
No eating, drinking or smoking where radioactive materials are in use
Wash your hands thoroughly after exposure of to any radioactive materials
Any cuts in the body should be covered before using radioactive sources
Arrange the source during experiments such that the radiation window points away from your
body
There are ten golden rules for working safely with radioactivity.
Rule Other considerations
1. Understand the nature
of the hazard and get
practical training.
Never work with unprotected cuts or breaks in the skin, particularly on
the hands or forearms. Never use any mouth operated equipment in any
area where unsealed radioactive material is used. Always store
compounds under the conditions recommended. Label all containers
clearly indicating nuclide, compound, specific activity, total activity,
date and name of user. Containers should be properly sealed.
2. Plan ahead to
minimize time spent
handling radioactivity.
Do a dummy run without radioactivity to check your procedures. The
shorter the time the smaller the dose.
3. Distance yourself
appropriately from
sources of radiation.
Doubling the distance from the source quarters the radiation dose
[Inverse square law].
4. Use appropriate
shielding for the
radiation.
1 cm Perspex will stop all betas but beware of bremsstrahlung x-rays
from high energy beta emitters. Use a suitable thickness of lead for X
and gamma emitters.
5. Contain radioactive
materials in defined
work areas.
Always keep active and inactive work separated as far as possible,
preferably by maintaining rooms used solely for radioactive work.
Always work over a spill tray and work in a ventilated enclosure except
with small (a few tens of MBq) quantities of 3H, 35S, 14C and 125I
compounds in a non-volatile form in solution.
6. Wear appropriate
protective clothing and
dosimeters.
For example, laboratory coats, safety glasses, surgical gloves and closed
top footwear. However beware of static charge on gloves when handling
fine powders. Local rules will define what dosimeters should be worn
e.g. body film badge, thermoluminescent extremity dosimeter for work
with high energy beta emitters, etc.
7. Monitor the work area
frequently for
In the event of a spill - follow the prepared contingency plan:
verbally warn all people in the vicinity
154
contamination control. restrict unnecessary movement into and through the area
report the spill to the School Radiation Safety Officer
treat contaminated personnel first
follow clean up protocol.
8. Follow the local rules
and safe ways of
working.
Do not eat, drink, smoke or apply cosmetics in an area where unsealed
radioactive substances are handled. Use paper tissues and dispose of
them appropriately. Never pipette radioactive solutions by mouth.
Always work carefully and tidily.
9. Minimise
accumulation of waste
and dispose of it by
appropriate routes.
Use the minimum quantity of radioactivity needed for the investigation.
Disposal of all radioactive waste is subject to statutory control. Be
aware of the requirements and use only authorised routes of disposal.
10. After completion
of work – monitor
yourself, wash and
monitor again
Never forget to do this. Report to the School Radiation Safety Officer if
contamination is found.
Table 5. 5
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5.6 END UNIT ASSESSMENT
5.6.1 Multiple choice questions
Instructions: Write number 1 to 5 in your notebook. Beside each number, write the letter
corresponding to the best choice
1. Radionuclides
A. Are those nuclides having more neutrons than protons
B. May emit X-rays.
C. Decay exponentially
D. May be produced in a cyclotron
2. Concerning Compton Effect:
A. There is interaction between a photon and a free electron.
B. The larger the angle through which the photon is scatted, the more energy it loses.
C. The wavelength change produced depends upon the scattering material.
D. High energy radiation is scatted more than lower energy radiations.
E. The amount of scattering that occurs depends on the electron density of the scattering material.
3. Classical physics offered a satisfactory explanation for
A. The diffraction of electrons by crystals
B. The deflection of charged particles in an electric field
C. The intensity spectrum of black body radiation
D. The photoelectric effect
E. Matter waves
4. When investigating β decay, the neutrino was postulated to explain
A. Conservation of the number of nucleons
B. Counteracting the ionizing effect of radiation
C. Conservation of energy and momentum
D. The production of antiparticles
E. The energy to carry away the β particles.
5. Gamma radiations differ from α and β emissions in that
A. It consist in photons rather than particles having nonzero rest mass
B. It has almost no penetrating ability
C. Energy is not conserved in the nuclear decays producing it
D. Momentum is not conserved in the nuclear decays producing it
E. It is not produced in the nucleus
6. The process represented by the nuclear equation 𝑇ℎ → 𝑅𝑎 + 𝐻𝑒24
88226
90230 is
A. Annihilation C. β decay E. γ decay
156
B. α decay D. pair production
7. Write number (i) to (iii) in your note book. Indicate beside each number whether the
corresponding statement is true (T) or false (F). If it is false, write a corrected version.
i. An alpha particle is also called a hydrogen nucleus
ii. The neutrino was suggested to resolve the problem of conserving energy and momentum in β
decay.
iii. The amount of energy released in a particular α or β decay is found by determining the mass
difference between the products and the parent. A mass-energy equivalence calculation then gives
the energy.
iv. The average biding energy per nucleon decreases with the increasing atomic mass number
8. A radioactive source emits radiations alpha, beta and gamma a shown below:
Fig.5. 17 Absorption of radiation
The main radiation(s) in the beam at X and Y are
Position X Position Y
A Alpha and beta Beta
B Beta and gamma Beta
C Alpha and gamma Gamma
D Alpha and beta Alpha
E Beta and gamma Gamma Table 5. 6 Radiation
9. The energy released by the nuclear bomb that destroyed Hiroshima was equivalent to 12.4 kilotons
of TNT. This is equivalent to 9.1 × 1026 MeV. The mass that was Converted into energy in this
explosion was (Convert MeV in Joules, use E=mc2)
A. 1.6 kg D. 1.1 × 1010 kg
B. 1.6 × 10–3 kg E. 120 kg
C. 1.4 × 1014 kg
10. In the decay scheme (Conserve charge and electron lepton number) the blanks should contain
𝑃 → 𝐷𝑍−1𝐴 + _______________ + __________________𝑍
𝐴
A. β+ and n D. β+ and ν
157
B. β- and ν E. β+ and β-
C. β- and p
11. Complete the following sentences by using a word, number and an equation where necessary
a) The half-life in years of the decay represented by the graph in fig.5…is___________
Fig.5. 18 Half life carve
b) When an animal or plant dies, no more _______________is taken in and that which is present
undergoes radioactive decay. If we measure the amount of carbon-14 left, it is possible to determine
the________ of the sample.
c) If an atom of material Y emits a gamma ray (gamma photon), then the nuclear reaction can be
represented symbolically as_________________
5.6.2 Structured questions
12. Prepare a table summarizing the three types of radioactive emission. Classify each type under the
following headings: Type of Emission, Mass, Charge, penetrating Power and Ionization Ability.
13. Copy the following table in your notebook and answer the questions that follow
a) What are the properties of alpha
radiation?
b) How do you calculate the half-life from
a graph?
c) What is the difference between
contamination and irradiation?
d) How should radioactive samples be
handled safely?
14. Give the value of 𝑥 and 𝑦 in each of the following equations
A. yBiPbx 212
83
212 D. xPbP 211
82
215
84 0
B. ePoBi x
y
0
1
214
83 E. yxH 3
1
C. HeRnRax
y
4
2
222
86
158
15. Give the value of x and y in each of the reaction classify each as , , or decay.
A. eBiPb 0
1
212
82
212
82 C. xThAc 227
90
227
89
B. ePbPo y
x
0
1
210
84 D. yRaRa y
x 226
88
16. The half-life of carbon14 is 5730 years the mass of certain sample of this isotope is g800 .
Graph the activity for the first 5 half-lives.
17. Beams of , - and radiation of approximately the same energy pass through electric and
magnetic fields as shown below.
Fig.5. 19 Deflection of radiations
A. Show the path taken by each particle in the two fields. Why do they follow these paths?
B. Which particle is the most penetrating? Explain your answer.
C. Which has the highest ionizing power?
D. How are -, + and electrons different?
E. How are x-rays, rays and photons different?
18. We are exposed to radiation all the time, indoors and outdoors. This is called background
radiation.
A. Give two examples of sources of this background radiation.
B. Which organ generally receives the most background radiation, and why?
C. There is some concern at the moment that pilots and flight attendants may have significantly
higher exposures to radiation than the normal exposure rates for the general public.
D. Why do pilots have a higher exposure to radiation than most other people?
19. Nuclei can decay by emitting particles which can change the energy, mass and charge of the
nucleus.
A. How is decay possible when the particle must pass an energy barrier which is greater than
the energy of the particle? Describe the process involved.
B. If isotope A emits particles with greater energy than isotope B (of the same element), which
will have the longer half-life?
C. How can a nucleus change its charge without emitting a charged particle?
20. Nuclear power is used in many places in the world. There are over 400 nuclear power plants
currently in operation, over 100 of which are in the USA, providing 20% of the electricity consumed
in that country. These plants use uranium fuel ( U238
92 enriched with 3% U235
92 ) to produce electricity. It
is the fission of the U235
92 nuclei which provides the majority of the thermal energy that is used to
generate the power.
159
A. Complete the following decay equation: U235
92 + n 37
93Rb 55
141Cs ____
B. Use the data in the table below to find the energy released in this reaction.
C. How many decays per second would it take to run a 60 W light globe?
D. If a power plant only converts 10% of the excess mass into useful energy, how many decays per
second would you need?
Useful masses:
Particles 92
235U
37
93Rb Cs141
55 42
Mass (amu) 235.04392 92.92172 140.91949 4.002603 0.000545 0.0000000
1 amu = 1.660566 10-27 kg.
5.6.3 Question of research
21. Using the information in radioactivity and making an internet search or/ and using other sources
of information, consolidate your skills in other hazardous materials you may meet in your area. Then
complete the table below (not exhaustive):
Types of compounds +description Symbol Risks Precautions
Compressed gas
Material that is normally gaseous and kept in a
pressurized container.
Flammable and combustible materials
Material that continue to burn when exposed to
a flame or near an ignition source
Toxic materials immediate and severe
Poisons and fatal materials that cause severe
and immediate harm
Bio hazardous infectious materials
Infectious agents or biological toxin causing a
serious disease and death
Corrosive materials
Materials which react with metals and living
tissue
Table 5. 7 Precaution signs
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UNIT 6: APPLICATIONS OF OPTICAL FIBER IN
TELECOMMUNICATION SYSTEMS.
Key unit Competence
By the end of this unit, I should be able to differentiate optical fiber transmission and other
transmitting systems.
My goals
Explain the functioning of optical fiber
Explain attenuation in optical fiber
Identify and explain the components of optical fiber system
Solve problem related to attenuation giving answers in decibels
Describe telecommunication system
Describe functions of amplifiers in optical fiber transmission
Distinguish optical fiber and other telecommunication systems
INTRODUCTORY ACTIVITY
Investigating the use of optical fiber in RWANDA
Rwanda plans to connect three million people to the World Wide Web as part of the "Internet for
All" project. The project is a World Economic Forum initiative that aims to connect 25 million new
Internet users in Kenya, Uganda, South Sudan and Rwanda by 2019.
161
This goal will partly be achieved by addressing the challenges of affordability, digital skills gap, lack
of local content and limited infrastructure, which are hindering growth in the use of Internet across
the region (http://www.threastafrican.co.ke, 2017)
Fig.6. 1: The installation and use of optical fiber in Rwanda
Following to the information provided above, answer to the following questions:
1. Observe the images A, B and C (Fig.6.1) and describe what you can see.
2. What are the uses of optical fiber in transmission of signals?
3. How do optical fibers function? In which field?
4. Discuss other applications of optical fibers.
6.1 PRINCIPLES OF OPERATIONS OF OPTICAL FIBERS
Activity 6.1: Total internal reflection in optical fiber.
Fig.6. 2: The total internal reflection in the optical fiber
Given the illustration above (Fig.6.2), one can see different rays inside the optical fiber. As the angle
of incidence in the core increases, as the angle of refraction increases more until it becomes right
angle at a certain value of incidence angle called critical angle. Discuss:
1. What do you understand by the term critical angle?
2. What causes the total internal reflection?
3. Discuss different fields where total internal reflection can be useful.
6.1.1 Definition
An optical fiber (fiber optics) is a medium for carrying information from one point to another in the
form of light. It uses a flexible, transparent fiber made by drawing glass or plastic and has a diameter
162
slightly thicker than that of a human hair. They are arranged in bundles called optical cables and can
be used to transmit signals over long distances.
Fiber optics continues to be used in more and more applications due to its inherent advantages over
copper conductors.
Fig.6. 3: An optical cable and a bundle of optical fibers
An optical fiber is made of 3 concentric layers:
Core: This central region of the optical fiber is made of silica or doped silica. It is the light
transmitting region of the fiber.
Cladding: This is the first layer around the core. It is also made of silica, but not with the same
composition as the core. This creates an optical waveguide which confines the light in the core by
total internal reflection at the core-cladding interface.
Coating: The coating is the first non-optical layer around the cladding. The coating typically
consists of one or more layers of polymer that protect the silica structure against physical or
environmental damage.
Fig.6. 4: the structure of optical fiber
The light is guided down the core of the fiber by the optical cladding which has a lower refractive
index. Remember that the refractive index is the ratio of the velocity of light in a vacuum to its
velocity in a specified medium. Then light is trapped in the core through total internal reflection. The
other outer parts that are the strength member and the outer jacket, serve as protectors.
Connecting two optical fibers is done by fusion splicing or mechanical splicing. It requires special
skills and interconnection technology due to the microscopic precision required to align the fiber
cores.
163
6.1.2 Refractive index of light
When light falls at the interface (boundary) of two media, it is partially reflected and partially
refracted. As it passes from one medium to another it changes its direction.
Fig.6. 5: Refraction of light from air to water and water to air for comparison.
The change in its direction is associated with the change in velocity. The ratio of the speed of light in
the vacuum c (or air) and that of light in a certain medium v is called the absolute refractive index n.
v
cn (6.01)
6.1.3 Total internal reflection
When light passes from one a medium of higher index of refraction into a medium of lower
refractive index the light bends away from the normal as indicated on Fig.6.6. A weak internally
reflected ray is also formed and its intensity increases as the incident angle increases.
Fig.6. 6: Illustration of total internal reflection
Increasing the angle of incidence increases the angle of refraction and at a particular incidence, the
angle of refraction reaches the 90°. This particular incident angle is called the critical angle 𝜃𝐶 . As
164
the incident angle exceeds the critical angle, the incident beam reflects on the interface between the 2
media and return in the first medium. This effect is called total internal reflection.
For any two media, using Snell’s law the critical angle is calculated using the expression
sinqc=n
2
n1
, (6.02)
where n1 and n2 are respectively the refractive indices of the first and second media.
𝜃𝐶 increases when 𝑛2 approaches 𝑛1.
1. Applying the above relation to the critical ray at a glass-air boundary we have where index of
glass is ng =1.50.
answer
0422/3
1sin CC
2. A beam of light is propagating through diamond, n = 2.42 and strikes a diamond-air interface at
an angle of incidence of 28°.
a) Will part of the beam enter the air or will the beam be totally refracted at the interface?
b) Repeat part (a) assuming that diamond is surrounded by water, n = 1.33
Answer:
a. 04.2442.2
1sin CC
Since 28° is greater than C , total internal reflection will occur, there is no refraction.
b. 03.3342.2
33.1sin CC
Since 28° is less than C some light will undergo refraction into the water.
Application:
An optical fiber is basically made of 2 types of glass put together in a concentric arrangement so the
middle is hollow. The inner circle of glass also called the Core consists of a glass of higher refractive
index than the outside layer as indicated on fig.6.4.
Example 6.1
165
Fig.6. 7: Total internal reflection in optical fiber as the angle of incidence 𝜽 is greater than the critical angle.
The outer layer of glass, which is also known as the optical cladding, does not carry light but is
essential to maintain the critical angle of the inner glass. The underlying main physics concept
behind the functioning of an optical fiber is a phenomenon known as total internal reflection.
Any light entering the fiber will meet the cladding at an angle greater than the critical angle. If light
meets the inner surface of the cladding or the core - cladding interface at greater than or equal to
critical angle then total internal reflection (TIR) occurs. So all the energy in the ray of light is
reflected back into the core and none escapes into the cladding. The ray then crosses to the other side
of the core and, because the fiber is more or less straight, the ray will meet the cladding on the other
side at an angle which again causes the total internal reflection. The ray is then reflected back across
the core again and again until it reaches the end of the optical fiber.
Maximum angle of incidence
The maximum angle of incidence in air for which all the light is total reflected at the core-cladding
is given by:
(6.03)
Example 6.1
1. An optical fibre consists of an inner material (the fiber) with refractive index nf and an outer
material of lower refractive index nc, known as cladding, as in Fig. 6.6 below.
Fig.6. 6
(a) What is the purpose of cladding?
(b) Show that the maximum acceptance angle θmax is given by
2
2
2
1sin nn
22
max0 sin cf nnn
166
(c) Discuss two main fiber loss mechanisms.
Answer
(a) The purpose of the cladding is to improve the transmission efficiency of the optical fibre. If
cladding is not used then the signal is attenuated dramatically.
b) Let a ray be incident at an angle , Fig.6.6, the angle of refraction at P being . Let C be the
critical angle at Q, interface of core and cladding (in this case 𝜃𝑐 = 𝜃𝑚𝑎𝑥)
Refraction from air to core:𝑛0 𝑠𝑖𝑛𝜃𝑚𝑎𝑥 = 𝑛𝑓𝑠𝑖𝑛𝜃𝑃 ↔ 𝑠𝑖𝑛𝜃𝑝 =𝑠𝑖𝑛𝜃𝑚𝑎𝑥
𝑛𝑓 (1)
Refraction from core to cladding: 𝑛𝑓 sin 𝐶 = 𝑛𝑐 sin 90 ↔ sin 𝑐 =𝑛𝑐
𝑛𝑓 (2)
Also so (3)
From (1) and (2) and using trigonometrically relation: 𝑐𝑜𝑠2𝐶 + 𝑠𝑖𝑛2𝐶 = (𝑛𝑐
𝑛𝑓)2 + (
𝑠𝑖𝑛𝜃𝑐
𝑛𝑓)2=1
Simplifying sin 𝜃𝑚𝑎𝑥 = ±√(𝑛𝑓2 − 𝑛𝑐
2)
This shows that there is a maximum angle of acceptance cone outside of which entering rays will
not be totally reflected within the fiber. For the largest acceptance cone, it is desirable to choose the
index of refraction of the cladding to be as small as possible. This is achieved if there is no
cladding at all. However, this leads to other problems associated with the loss of intensity.
(c) The transmission is reduced due to multiple reflections and the absorption of the fibre core
material due to impurities.
2: A step-index fiber 0.01 cm in diameter has a core index of 1.53 and a cladding index of 1.39. See
Fig.6.7. Such clad fibers are used frequently in applications involving communication, sensing, and
imaging.
Fig.6. 7
What is the maximum acceptance angle θm for a cone of light rays incident on the fiber face such
that the refracted ray in the core of the fiber is incident on the cladding at the critical angle?
Answer:
p
cp 90 cp cossin
167
First find the critical angle θc in the core, at the core-cladding interface. Then, from geometry,
identify θr and use Snell’s law to find θm.
(1) Refraction from the core to cladding interface:
(2) From right-triangle geometry, θr = 90 − 65.3 = 45.7°
(3) From Snell’s law, at the fiber face,
And
Thus, the maximum acceptance angle is 39.7° and the acceptance cone is twice that, 2 θm = 79.4°.
The acceptance cone indicates that any light ray incident on the fiber face within the acceptance
angle will undergo total internal reflection at the core-cladding face and remain trapped in the fiber
as it propagates along the fiber.
6.1.4 Checking my progress
1. Operation of optical fiber is based on:
A. Total internal reflection
B. Total internal refraction
C. Snell’s law
D. Einstein’s theory of reality
E. None of the above
2. When a beam of light passes through an optical fiber
A. Rays are continually reflected at the outside(cladding) of the fiber
B. Some of the rays are refracted from the core to the cladding
C. The bright beam coming out of the fiber is due to the high refractive index of the core
D. The bright beam coming out of the fiber is due to the total internal reflection at the core-cladding
interface
E. All the rays of light entering the fiber are totally reflected even at very small angles of incidence
3. A laser is used for sending a signal along a mono mode fiber because
A. The light produced is faster than from any other source of light
B. The laser has a very narrow band of wavelengths
C. The core has a low refractive index to laser light
D. The signal is clearer if the cladding has a high refractive index
E. The electrical signal can be transferred quickly using a laser
4. Given that the refractive indices of air and water are 1 and 1,33, respectively, find the
critical angle.
03.6553.1
39.1sin cc
rcoremair nn sinsin
00 7.397.24sin00.1
53.1sinsin m
air
core
mn
n
168
5. The frequency of a ray of light is 6.0x1014 Hz and the speed of light in air is 3x108 m/s. the
refractive index of the glass is 1.5.
a) Explain the meaning of refracting index
b) A ray of light has an angle of incidence of 30° on a block of quartz and an angle of refraction of
20°. What is the index of refraction of the quartz?
6. A beam of light passes from water into polyethylene (n = 1.5). If θi = 57.5°, what is the angle of
refraction?
7. (a) What is the critical angle when light is going from a diamond (n= 2.42) to air?
(b)Using the answer to (a), what happens when:
(i)The angle of incidence is less than that angle?
(ii) The angle of incidence is more than that angle?
169
6.2 TYPES OF OPTICAL FIBERS
Activity 6.2: Investigating the types of optical fiber.
Use search internet and discuss different types of optical fiber. Then, differentiate them according to
their respective uses.
There are three main types of Optical Fibers: Monomode (or single mode), Multimode and special
purpose optical fibers.
6.2.1 Monomode fibers
Those are Fibers that support a single mode and are called single-mode fibers (SMF). Single-mode
fibers are used for most communication links longer than 1 000 m.
Fig.6. 8: Structure of monomode or single-mode optical fiber
In the monomode fiber, the core is only about 8 μm in diameter, and only the straight through
transmission path is possible, i.e. one mode. This type, although difficulty and expensive to make, is
being used increasingly. For short distances and low bit-rates, multimode fibers are quite
satisfactory.
Following the emergence of single-mode fibers as a viable communication medium in
1983, they quickly became the dominant and the most widely used fiber type within
Telecommunications. Major reasons for this situation are as follows:
1. They exhibit the greatest transmission bandwidths and the lowest losses of the fiber transmission
media.
2. They have a superior transmission quality over other fiber types because of the
absence of modal noise.
3. They offer a substantial upgrade capability (i.e. future proofing) for future wide- bandwidth
services using either faster optical transmitters or receivers or advanced transmission techniques
(e.g. coherent technology,).
4. They are compatible with the developing integrated optics technology.
5. The above reasons 1 to 4 provide confidence that the installation of single-mode fiber will
provide a transmission medium which will have adequate performance such that it will not
require replacement over its anticipated lifetime of more than 20 years. (John, 2009)
6.2.2 Multimode fibers
In multimode fiber, light travels through the fiber following different light paths called “modes” as
indicated on Fig.6.9. Those are fibers that support many propagation paths. A multi-mode optical
170
fiber has a larger core of about 50 μm, allowing less precise, cheaper transmitters and receivers to
connect to it as well as cheaper connectors.
Fig.6. 9 Multimode optical fiber
The propagation of light through a multimode optical fiber is shown on Fg. 6.9. However, a multi-
mode fiber introduces multimode distortion, which often limits the bandwidth and length of the link.
Furthermore, because of its higher dopant content, multi-mode fibers are usually expensive and
exhibit higher attenuation.
There are two types of multi-mode optical fibers: multimode step-index and multimode graded index
(see Fig.6.10)
Fig.6. 10: Step index and graded index multimode optical fibers illustration.
In step-index multimode type, the core has the relatively large diameter of 50μm and the
refractive index changes suddenly at the cladding. The wide core allows the infrared to travel by
several paths or modes. Paths that cross the core more often are longer, and signals in those modes
take longer to travel along the fiber. Arrival times at the receiver are therefore different for
radiation of the same pulse, 30ns km-1, being a typical difference. The pulse is said to suffer
dispersion, it means that it is spread out.
In the graded index multimode type, the refractive index of the glass varies continuously from
a higher value at the center of the fiber to a low value at the outside, so making the boundary
between core and the cladding indistinct. Radiation following a longer path, travel faster on
average, since the speed of light is inversely proportional to the refractive index. The arrival times
for different modes are the about the same (to within 1ns km-1) and all arrive more or less together
at the receiving end. Dispersion is thereby much reduced.
6.2.3 Special-purpose optical fiber
Some special-purpose optical fiber is constructed with a non-cylindrical core and/or cladding layer,
usually with an elliptical or rectangular cross-section. These include: polarization-maintaining
fiber and fiber designed to suppress whispering gallery mode propagation.
171
Polarization-maintaining fiber is a unique type of fiber that is commonly used in fiber optic
sensors due to its ability to maintain the polarization of the light inserted into it.
Photonic-crystal fiber is made with a regular pattern of index variation. It is often in the form of
cylindrical holes that run along the length of the fiber. Such fiber uses diffraction effects in
addition to total internal reflection, to confine light to the fiber's core.
6.2.4 Checking my progress
1. Fiber optics is best known for its application in long-distance telecommunications.
a) True
b) False
2. Choose the basic types of optical fiber:
A. Single-mode E. Multi-mode
B. X-mode F. A and C
C. Microwave-mode G. B and D
D. Graded-index mode H. A and E
3. Single-mode fiber has the advantage of greater bandwidth capability. It has the disadvantage of:
A. Being harder to bend
B. Smaller mechanical tolerances in connectors and splices
C. Being difficult to couple light into
D. B and C
E. None of the above
4. Describe with the aid of simple ray diagrams:
A. The multimode step index fiber;
B. The single-mode step index fiber.
C. Compare the advantages and disadvantages of these two types of fiber for use as an optical
channel.
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6.3 MECHANISM OF ATTENUATION
Activity 6.3: Light transmission analysis in optical fiber
Fig.6. 11 The images to show the attenuation in optical fiber
Observe the image clearly, and answer to the following questions:
1. Does all the light from the source getting to the destination?
2. What do you think is causing the loss in light transmission?
3. What can be done to minimize that loss in the optical fibers above?
Attenuation in fiber optics, also known as transmission loss, is the reduction in intensity of the light
beam (or signal) as it travels through the transmission medium. Over a set distance, fiber optic with a
lower attenuation will allow more power to reach its receiver than a fiber with higher attenuation.
Attenuation can be caused by several factors both extrinsic and intrinsic:
Intrinsic attenuation is due to something inherent to the fiber such as impurities in the glass
during manufacturing. The interaction of such impurities with light results in the scattering of
light or its absorption.
Extrinsic attenuation can be caused by macro bending and micro lending. A bent imposed on an
optical fiber produce a strain in that region of the fiber and affects its refractive index and the
critical angle of the light ray in that area. Macro bending that is a large-scale bent and micro
bending which is a small-scale bent and very localized are external causes that result in the
reduction of optical power.
Attenuation coefficients in fiber optics usually are expressed decibels per kilometer (dB/km) through
the medium due to the relatively high quality of transparency of modern optical transmission media.
It is observed that the attenuation is a function of the wavelength of the light. The attenuation )( tot
at wavelength λ of a fiber between two cross-sections, 1 and 2, separated by distance Lis defined, as
)(
)(log
10)(
2
1
P
P
Ltot (6.04)
where )(1 P optical power at the cross-section 1, and )(2 P the optical power at the cross-section 2.
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Attenuation is an important limiting factor in the transmission of a digital signal across large
distances. Thus, much research has gone into both limiting the attenuation and maximizing the
amplification of the optical signal.
6.3.1 Light scattering and absorption
In the light transmission of signals through optical fibers, attenuation occurs due to light scattering
and absorption of specific wavelengths, in a manner similar to that responsible for the appearance of
color.
(a) Light scattering
Fig.6. 12: Light scattering in optical fiber.
The propagation of light through the core of an optical fiber is based on total internal reflection of the
light wave. Rough and irregular surfaces, even at the molecular level, can cause light rays to be
reflected in random directions as it is illustrated on Fig.6.12. This is called diffuse
reflection or scattering, and it is typically characterized by wide variety of reflection angles.
Light scattering depends on the wavelength of the light being scattered. Thus, limits to spatial scales
of visibility arise, depending on the frequency of the incident light-wave and the physical dimension
(or spatial scale) of the scattering center, which is typically in the form of some specific micro-
structural feature. Since visible light has a wavelength of the order of one micrometer (one millionth
of a meter) scattering centers will have dimensions on a similar spatial scale. Thus, attenuation
results from the incoherent scattering of light at internal surfaces and interfaces.
(a) Light absorption
Material absorption is a loss mechanism related to the material composition and fiber fabrication
process. This results in the dissipation of some transmitted optical power as heat in the waveguide.
Absorption is classified into two basic categories: Intrinsic and extrinsic absorptions. (John, 2009)
Intrinsic absorption: is caused by basic fiber material properties. If an optical fiber is absolutely
pure, with no imperfections or impurities, ten all absorption will be intrinsic. Intrinsic absorption
in the ultraviolet region is caused bands. Intrinsic absorption occurs when a light particle (photon)
interacts with an electron and excites it to a higher energy level.
Extrinsic absorption is caused by impurities caused by impurities introduced into the fiber
material. The metal impurities such as iron, nickel and chromium are introduced into the fiber
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during fabrication. Extrinsic absorption is caused by electronic transition of these metal ions from
one energy level to another level.
6.3.2 Measures to avoid Attenuation
The transmission distance of a fiber-optic communication system has traditionally been limited by
fiber attenuation and by fiber distortion.
Repeaters: Repeaters convert the signal into an electrical signal, and then use a transmitter to
send the signal again at a higher intensity than was received, thus counteracting the loss incurred
in the previous segment. They mostly used to be installed about once every 20 km.
Regenerators: Optical fibers link, in common with any line communication system, have a
requirement for both jointing and termination of the transmission medium. When a
communications link must span at a larger distance than existing fiber-optic technology is capable
of, the signal must be regenerated at intermediate points in the link by optical communications
repeaters called regenerators. An optical regenerator consists of optical fibers with special coating
(doping). The doped portion is pumped with a laser. When the degraded signal comes into the
doped coating, the energy from the laser allows the doped molecules to become lasers themselves.
The doped molecules then emit a new strong light signal with the same characteristics as the
incoming weak signal. Basically, the regenerator is a laser amplifier for the incoming signal.
Optical Amplifiers: Another approach is to use an optical amplifier which amplifies the optical
signal directly without having to convert the signal into the electrical domain. It is made
by doping a length of fiber with the rare-earth mineral erbium and pumping it with light from
a laser with a shorter wavelength than the communications signal (typically 980 nm). Amplifiers
have largely replaced repeaters in new installations.
6.3.3 Checking my progress
1. True or False: One of the reasons fiber optics hasn’t been used in more areas has been the
improvement in copper cable such as twisted pair.
2. True or False: With current long-distance fiber optic systems using wavelength-division
multiplexing, the use of fiber amplifiers has become almost mandatory.
3. Fiber optics has extraordinary opportunities for future applications because of its immense
bandwidth.
A. True
B. False
4. (a) What do we mean by attenuation in optical fibers?
(b) State two ways in which energy is lost in optical fibers.
(c) If a fiber loses 5% of its signal strength per kilometer, how much of its strength would be left
after 20 km?
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6.4 OPTICAL TRANSMITTER AND OPTICAL RECEIVER
Activity 6.4: Investigating the signal sources and signal receiver for optic fibers
With the basic information you know about the functioning process of optical fiber, answer to the
following questions.
1. Where does the light that is transmitted into the optical fiber core medium come from?
2. What are the type compositions of the light signal propagating into optical fiber?
3. Discuss and explain the function principle of signal generators and signal receivers of light from
optical fibers.
The process of communicating using fiber-optics involves the following basic steps:
1. Creating the optical signal involving the use of a transmitter, usually from an electrical signal.
2. Relaying the signal along the fiber, ensuring that the signal does not become too distorted or
weak.
3. Receiving the optical signal.
4. Converting it into an electrical signal.
Fig.6. 13: Optical fiber communication mechanism (Transmitter and receiver blocks).
6.4.1 Transmitters
The most commonly used optical transmitters are semiconductor devices such as light-emitting
diodes (LEDs) and laser diodes. The difference between LEDs and laser diodes is that LEDs
produce incoherent light, while laser diodes produce coherent light.
For use in optical communications, semiconductor optical transmitters must be designed to be
compact, efficient and reliable, while operating in an optimal wavelength range and directly
modulated at high frequencies (see Fig.6.13: Transmitter block).
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In its simplest form, a LED is a forward-biased p-n junction, emitting light through spontaneous
emission, a phenomenon referred to as electroluminescence. The emitted light is incoherent with a
relatively wide spectral width of 30–60 nm. LED light transmission is also inefficient, with only
about 1% of input power, or about 100 microwatts, eventually converted into launched power which
has been coupled into the optical fiber. However, due to their relatively simple design, LEDs are very
useful for low cost applications.
6.4.2 The Optical Receivers
The main component of an optical receiver is a photodetector (photodiode) which converts the
infrared light signals into the corresponding electrical signals by using photoelectric effect before
they are processed by the decoder for conversion back into information. The primary photo detectors
for telecommunications are made from Indium gallium arsenide (see Fig.6.13).
The photodetector is typically a semiconductor-based photodiode. Several types of photodiodes
include p-n photodiodes, p-i-n photodiodes, and avalanche photodiodes. Metal-semiconductor-
metal (MSM) photodetectors are also used due to their suitability for circuit
integration in regenerators and wavelength-division multiplexers.
6.4.3 Checking my progress
1. Circle the three basic components in a fiber optic communications system.
A. Telescope E. Maser fiber
B. Transmitter F. Optical fiber
C. Receiver G. Alternator
D. Surveillance satellites
2. Information (data) is transmitted over optical fiber by means of:
A. Light D. Acoustic waves
B. Radio waves E. None of the above
C. Cosmic rays
3. Connectors and splices add light loss to a system or link.
a) True
b) False
4. Do fibers have losses?
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6.5. USES OF OPTICAL FIBERS
Activity 6.5: Applications of fiber optics in telecommunication and in medicine
Use the internet or the library to investigate the applications of optical fiber in medicine and
telecommunication systems.
6.5.1 Telecommunications Industry
Optical fibers offer huge communication capacity. A single fiber can carry the conversations of every
man, woman and child on the face of this planet, at the same time, twice over. The latest generations
of optical transmission systems are beginning to exploit a significant part of this huge capacity, to
satisfy the rapidly growing demand for data communications and the Internet.
The main advantages of using optical fibers in the communications industry are:
- A much greater amount of information can be carried on an optical fiber compared to a copper
cable.
- In all cables some of the energy is lost as the signal goes along the cable. The signal then needs to
be boosted using regenerators. For copper cable systems these are required every 2 to 3km but
with optical fiber systems they are only needed every 50km.
- Unlike copper cables, optical fibers do not experience any electrical interference. Neither will
they cause sparks so they can be used in explosive environments such as oil refineries or gas
pumping stations.
- For equal capacity, optical fibers are cheaper and thinner than copper cables and that makes them
easier to install and maintain.
6.5.2 Medicine Industry
The advent of practicable optical fibers has seen the development of much medical technology.
Optical fibers have paved the way for a whole new field of surgery, called laproscopic surgery (or
more commonly, keyhole surgery), which is usually used for operations in the stomach area such as
appendectomies. Keyhole surgery usually makes use of two or three bundles of optical fibers. A
"bundle" can contain thousands of individual fibers". The surgeon makes a number of small incisions
in the target area and the area can then be filled with air to provide more room.
One bundle of optical fibers can be used to illuminate the chosen area, and another bundle can be
used to bring information back to the surgeon. Moreover, this can be coupled with laser surgery, by
using an optical fiber to carry the laser beam to the relevant spot, which would then be able to be
used to cut the tissue or affect it in some other way.
6.5.3 Checking my progress
The basic unit of digital modulation is:
A. Zero D. A and B
B. One E. None of the above
C. Two
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6.6 ADVANTAGES AND DISADVANTAGES OF OPTICAL FIBERS
Activity 6.6Advantages and disadvantages of optical fibers
Use search internet or your library to investigate the advantages and disadvantages of fiber optics.
Although there are many benefits to using optical fibers, there are also some disadvantages. Both are
discussed below:
6.6.1 Advantages
Capacity: Optical fibers carry signals with much less energy loss than copper cable and with a
much higher bandwidth. This means that fibers can carry more channels of information over
longer distances and with fewer repeaters required.
Size and weight: Optical fiber cables are much lighter and thinner than copper cables with the
same bandwidth. This means that much less space is required in underground cabling ducts. Also
they are easier for installation engineers to handle.
Security: Optical fibers are much more difficult to tap information from undetected; a great
advantage for banks and security installations. They are immune to electromagnetic interference
from radio signals, car ignition systems, lightning etc. They can be routed safely through
explosive or flammable atmospheres, for example, in the petrochemical industries or munitions
sites, without any risk of ignition.
Running costs: The main consideration in choosing fiber when installing domestic cable TV
networks is the electric bill. Although copper coaxial cable can handle the bandwidth
requirement over the short distances of a housing scheme, a copper system consumes far more
electrical power than fiber, simply to carry the signals.
6.6.2 Disadvantages
Price: In spite of the fact that the raw material for making optical fibers, sand, is abundant and
cheap, optical fibers are still more expensive per metre than copper. Having said this, one fiber
can carry many more signals than a single copper cable and the large transmission distances mean
that fewer expensive repeaters are required.
Special skills: Optical fibers cannot be joined together (spliced) as an easily as copper cable and
requires additional training of personnel and expensive precision splicing and measurement
equipment.
6.6.3 Checking my progress
1. List two advantages of using optical fiber. __________________________________
2. The replacement of copper wiring harnesses with fiber optic cabling will increase the weight of an
aircraft.
a) True
b) False
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6.7. END UNIT ASSESSMENT
1. (a) An endoscope uses coherent and non−coherent fiber bundle
(i) State the use of the coherent bundle and describe its arrangement of fibers.
(ii) State the use of the non−coherent bundle and describe its arrangement of fibers.
(b) Each fiber has a core surrounded by cladding. Calculate the critical angle at the core−cladding
interface.
Refractive index of core = 1.52
Refractive index of cladding = 1.
2. (a) Fig.6.9 shows a ray of light travelling through an individual fiber consisting of cladding and a
core. One part has a refractive index of 1.485 and the other has a refractive index of 1.511.
Fig.6. 9: Light transmission in optical fiber.
(i) State which part of the fiber has the higher refractive index and explain why.
(ii) Calculate the critical angle for this fiber.
(b) The figure below shows the cross-section through a clad optical fiber which has a core of
refractive index 1.50.
Fig.6. 10
Complete the graph below to show how the refractive index changes with the radial distance along
the line ABCD in the figure above.
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Fig.6. 11: Axes for the half life decay curve
3.(a) What do we mean by attenuation in optical fibers? (b) State two ways in which energy is lost
along the length of an optical fiber. (c) If a fiber loses 5% signal strength per km, how much strength
would be left after 20 km?
4. Estimate the length of time it would take a fiber optic system to carry a signal from the UK to the
USA under the Atlantic. (Take c = 2 x 108 m/s in the cable. Estimate the length of the cable under the
sea.)
a. Estimate the length of time it would take a microwave signal to travel from the UK to the USA a satellite
Enk. (Geosynchronous satellites orbit at a height of about 36 000 Ian above the Earth's surface.
b. Which would give less delay in a telephone conversation?
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UNIT 7: BLOCK DIAGRAM OF TELECOMMUNICATION
Key unit Competence
By the end of the unit I should be able to construct and analyze block diagram of telecommunication
systems.
My goals
Identify parts of a block diagram of telecommunication system.
Differentiate oscillator, modulator and amplifier.
Outline the function of a microphone and antenna.
Describe terms applied in telecommunication systems
Construct, analyse and judge block diagrams of a telecommunication system.
Realise that parts of a telecommunication system are dependent
INTRODUCTORY ACTIVITY
Investigating the function of wireless microphone
Materials:
- Wireless microphone set -Connecting wires
- Amplifier and mixer -Speaker
Procedure:
Connect the full sound system such that the signal will be transmitted to the speakers using wireless
microphone.
Questions:
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1. How your voice is getting to the speakers?
2. Where else this system is used?
3. What are advantages and disadvantages of communication?
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7.1 OPERATING PRINCIPLE OF MICROPHONE
Activity 7.1: Investigating the function of a microphone
Take the case of two people talking on telephone (see Fig.7.1). Observe the image above and answer
to the following questions:
Fig.7. 1 People talking on telephone
1. Discuss the functioning process of a telephone.
2. Differentiate the functions of a microphone from that of a speaker.
Telecommunication in real life is the transmission of signals and other types of data of any nature
by wire, radio, optical or other electromagnetic systems of communication. Telecommunication
occurs when the exchange of information between communicating participants includes the use of
signs or other technologically based materials such as telephone, TV set, radio receiver, radio
emitter, computer, and so on. All can be done either mechanically, electrically or electronically.
The use of microphones began with the telephone in the nineteenth century. The requirements were
basically those of speech intelligibility, and the carbon microphone, developed early in that art, is
still used in telephones today.
Particles of carbon are alternately compressed and relaxed by the diaphragm under the influence of
sound pressure, and the resulting alternation of resistance modulates the current proportionally to the
change in resistance. Carbon microphones are noisy; they have limited dynamic range and produce
high levels of distortion. However, none of these defects is really serious in its application to
telephony.
Operating principle of microphones
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A microphone converts sound vibrations into electrical entity. Basically a microphone has a
diaphragm which moves when sound pressure pushes it. This movement can be converted into
proportional voltage using several possible transducers.
Fig.7. 2: The outer and internal view of a microphone
A transducer is a device which receives electrical, mechanical or acoustic waves from one medium
and converts them into related waves for a similar or different medium. Thus, it can be said that a
microphone is a transducer that converts acoustical sound energy into electrical energy. Its basic
function is therefore to convert sound energy into electrical audio signals which can be used for
further processing. Microphones are classified based on construction and directivity.
7.2 CHANNELS OF SIGNAL TRANSMISSION
Activity 7.2: Investigating signal transmission
Basing on the activity 7.1, explain and discuss how the voices are transmitted from our mouth to
telephone and then to the receiver’s telephone
An audio frequency (acronym: AF) or audible frequency is characterized as a periodic vibration
whose frequency is audible to the average human. The SI unit of frequency is the hertz (Hz). It is the
property of sound that most determines pitch.
The generally accepted standard range of audible frequencies is 20Hz to 20 kHz, although the range
of frequencies that individuals hear is greatly influenced by environmental factors. Frequencies
below 20 Hz are generally felt rather than heard, assuming the amplitude of the vibration is great
enough. Frequencies above 20 kHz can sometimes be sensed by young people. High frequencies are
the first to be affected by hearing loss due to age and/or prolonged exposure to very loud noises.
Modulation is the process of superimpose to a low frequency signal (original signal) a high
frequency signal (carrier signal) for transmission. The resulting signal is a modulated or radio signal.
7.2.1 Amplitude modulation (AM)
It is a type of modulation, where the amplitude of the carrier wave is changed in accordance with the
intensity of the signal. However, the frequency and the phase shift of the modulated wave remains
the same.
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Fig.7. 3 A graphs of amplitude modulation
Note that the amplitudes of both positive and negative half-cycles of carrier wave are changed in
accordance with the signal. For instance, when the signal is increasing in the positive sense, the
amplitude of carrier wave also increases. On the other hand, during negative half-cycle of the signal,
the amplitude of carrier wave decreases. Amplitude modulation is done by an electronic circuit
called modulator.
7.2.2 Frequency modulation (FM).
It is a type of modulation, where the frequency of the carrier wave is changed in accordance with the
intensity of signal. The amplitude and the phase shift of the modulated wave remain the same. The
frequency variations of carrier wave depend upon the instantaneous amplitude of the original signals.
The carrier frequency increases and decreases respectively to its positive and negative peak values as
the voltage of the original signal seem to approach its peak values.
Fig.7. 4: Process of FM transmission
Comparison of amplitude modulation and frequency modulation
FM AM
The amplitude and phase shift of carrier wave The amplitude of carrier changes with
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remains constant with modulation modulation
The carrier frequency changes with modulation The carrier frequency and phase shift of carrier
wave remains constant with modulation
The carrier frequency changes according to the
strength of the modulating signal
The carrier amplitude changes according to the
strength of the modulating signal
Table 7. 1: Comparison between FM and AM
7.2.3 Short wave (SW)
A short wave is any wave whose frequency ranges between 300 kHz and 3 MHz. In transmission,
these waves are used for very long distance communication as their bands can be reflected or
refracted from the ionosphere by an electrically charged layer with atoms in the atmosphere.
Fig.7. 5: Short wave illustration
The short waves directed at an angle into the sky can be reflected back to Earth at great distances,
beyond the horizon. This called sky wave or skip propagation. These waves are used for radio
broadcasting of voice and music to shortwave listeners over very large areas; sometimes entire
continents or beyond. They are also used for military communication, diplomatic communication,
and two-way international communication by amateur radios enthusiasts for hobby.
7.2.4 Medium wave (MW)
Medium wave (MW) is the part of the medium frequency (MF) radio band used mainly for AM
radio broadcasting. It is the original radio broadcasting band, in use since the early 1920's. It is
typically used by stations serving a local or regional audience. At night, medium wave signals are no
187
longer absorbed by the lower levels of the ionosphere, and can often be heard hundreds or even
thousands of miles away.
For Europe the MW band ranges from 526.5 kHz to 1606.5 kHz, using channels spaced every 9 kHz,
and in North America an extended MW broadcast band ranges from 525 kHz to 1705 kHz, using 10
kHz spaced channels.
7.2.5 Checking my progress
1. In transmission, the range of short waves are between
A. Radio wave and microwave
B. X-rays and gamma rays
C. Infrared and visible light
D. Infrared and ultraviolet
2. Where Short waves can be used?
3. Explain what is meant by Medium wave (MW)
4. Distinguish between Amplitude modulation and frequency modulation
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7.3 CARRIER WAVE AND MODULATOR
7.3.1 Concept of carrier wave modulation
Activity 7.3: Modulation techniques
Fig.7. 6: Radio wave transmission
Observe the mechanism above (Fig.7.6) and answer to the following questions
1. Analyze the provided figure and explain the transmission process used there.
2. What are applications of such a system shown in the above figure?
Modulation is the process of varying the characteristics of carrier signal with the modulating signal
or modulation is defined as the superimposition of low frequency baseband signal (modulating
signal) over high frequency carrier signal by varying different parameters of the carrier signals (see
Fig.7.6). Based on the types of parameters that are varied in proportion to the baseband (low
frequency) signal, modulation is of different types.
In digital modulation, the message signal is converted from analog into digital. In digital
modulation techniques, the analog carrier signal is modulated by discrete signal. The carrier wave is
switched on and off to create pulses such that signal is modulated.
Low frequency signal (Baseband) communication is not commonly used for distance
communication. Low frequency baseband signals, having low energy, if transmitted directly will get
distorted. So baseband signal must be modulated with high frequency signal to increase the range of
transmission.
7.3.2 Checking my progress
1. In………transmission, the carrier signal modulated so that its amplitude varies with the changing
amplitudes of the modulating signal
189
A. AM C. FM
B. PM D. None of the above?
2. Distinguish between analog signal and digital signal
3. What is meant by carrier wave in telecommunication?
4. What is the application of a carrier wave in a telecommunication system?
190
7.4 OSCIALLATOR, RADIO FREQUENCY AMPLIFIER AND POWER
AMPLIFIER
Activity 7.4: Investigating what is an oscillator and a radio frequency amplifier
Make an intensive research on the properties and function of an oscillator and radio frequency
amplifier. According to your findings, answer to the following questions:
1. Explain a radio frequency amplifier and state its importance in telecommunication?
2. What do you understand by an oscillator in telecommunication system? Discus its importance?
3. Describe other uses of oscillator and radio frequency amplifier.
7.4.1 Oscillator
Oscillators are electronic circuits that produce a periodic waveform on its output with only the DC
supply voltage as an input. The output voltage can be either sinusoidal or non-sinusoidal,
depending on the type of oscillator, thus, the outputs signals can be sine waves, square waves,
triangular waves, and saw tooth waves.
Fig.7.7: Basic function of oscillator and radio frequency amplifier in telecommunication system
The oscillation in any circuit will depend on the following properties:
Amplification of the used amplifier
A frequency determining device (receiver/ transmitter)
Signal regeneration (Positive feedback)
Factors which may fluctuate the operating frequency
Long time of operation
Heat that is generated along the operation
Operating point of the active elements
Frequency dropper elements (capacitors, inductors)
Change in total opposition faced by the alternating current (impedance)
191
Oscillators may be classified in three ways, including:
(a) the design principle used where we have a positive and a negative feedback oscillators,
(b) the frequency range of the signal over which they are used:
Audio Frequency (AF) oscillators (frequency range is 20 Hz to 20 kHz)
Radio Frequency (RF) oscillators (frequency range is 20 kHz to 30 MHz)
Video Frequency oscillators (frequency range is dc to 5 MHz)
High Frequency (HF) oscillators (frequency range is 1.5 MHz to 30 MHz)
Very High Frequency (VHF) oscillators (frequency range is 30 MHz to 300 MHz)
(c) the nature of generated signals where we have:
Sinusoidal Oscillators: These are known as harmonic oscillators and are generally LC tuned-
feedback or RC tuned-feedback type oscillator that generates a sinusoidal waveform which is of
constant amplitude and frequency.
Non-sinusoidal Oscillators: These are known as relaxation oscillators and generate complex non-
sinusoidal waveforms that changes very quickly from one condition of stability to another such as
square-wave, triangular-wave or sawtooth-wave type waveforms.
Fig.7. 8: Types of signals output of an oscillator
The oscillators have a variety of applications. In some applications we need voltages of low
frequencies, in others of very high frequencies. For example to test the performance of a stereo
amplifier, we need a signal of variable frequency in the audio range (20 Hz-20 KHz). Next to
amplifiers, oscillators are the most important analog circuit block. Oscillators can be found in almost
every imaginable electronic system. For example all radio receiving systems must have a local
oscillator. All transmitting systems require oscillators to define the carrier frequency. Similarly, most
digital systems are clocked and require a master clock oscillator to operate. Signal sources, which are
essential for testing electronic systems, are also precise oscillators whose frequency and amplitude
can be accurately set according to the requirement.
7.4.2 Radio frequency amplifier
An amplifier is an electronic device which can increase the amplitude or the power of the input
signal to its input parts, without the needs of modifying the form of that signal. Mostly, these devices
are used in telecommunication, especially in receivers. Any amplifier has an active element, more
often transistors, though there may exist also resistors, inductors and capacitors.
192
Classes of amplifiers
There exist two classes: Capacitor coupled amplifiers and transformer coupled amplifiers. The
two are used in multistage amplifiers, that is when we connect two stage amplifiers using a capacitor
and when we connect two stages amplifiers using a transformer, we get a capacitor coupled amplifier
and a transformer coupled amplifier respectively.
Characteristics of RF amplifier
1. It may require or not a wide bandwidth signal to amplify
2. The output signal from the RF amplifier may or not be linear
3. They require to operate at a narrow bandwidth
4. They can use filters to reduce bandwidth
5. To tune the circuit, the resonant frequency is set to LC
fo2
1
All electronic devices have an inductive reactance and capacitive reactances. The latter are vary as
the frequency fluctuates. Normally, as the frequency increases, the inductive reactance increases but
capacitive reactance decreases. Then the circuit will be called self-resonate at point, where the two
characteristics mentioned above become equal.
In signal processing, we need to realize as many operations as possible so that we arrive to a signal
that fits the transmission standards. The signal to be modulated is referred to as a baseband signal.
The carrier signal needs to be a higher frequency than the baseband. A RF amplifier is a device
which amplifies the baseband signal. However, devices such as Oscillators, Mixers, Multipliers and
frequency synthesizers can be used to meet the above conditions.
7.4.3 Power Amplifier
Signals are amplified in several stages (Fig.7.10). The initial stages are small signal amplifiers, they
are designed to give good voltage gain, so they are called voltage amplifiers. At the final stage, the
signal becomes large, the large-signal amplifier is called power amplifier, as it is designed for good
power gain.
Fig.7. 9 The functioning mechanism of power amplifier
The Fig.7.11 shows that the power amplifiers are classified according to the conduction angle they
produced. Conduction angle measures the portion of the input cycle that is reproduced at the output
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of a power amplifier. If the conduction angle is 360°, which means that all of the input cycle is
reproduced, the amplifier is called class A amplifier.
Fig.7. 10: The conduction angle of power amplifier
Every amplifier has a DC equivalent circuit and an AC equivalent circuit. Because of this, it has
two load lines : a Dc load line and an AC load line.
7.4.4 Checking my progress
1. State the classifications of oscillators according to Frequency Band of the Signals
2. Explain what is mean by Oscillator
3. The figure is about transmission of signals in telecommunication. Study it carefully and label it.
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7.5 ANTENNAS
Activity 7.5: Defining types of antennas
Observe clearly the images on the fig. 7.13 below and answer the questions that follow:
Fig.7. 11 Different types of antenna
1. Describe the different the types of antenna shown in the Fig.7.13 above.
2. Discuss other different types of antenna you know.
3. Discuss and explain the function principle of an antenna.
An antenna or aerial is an electrical device connected (often through a transmission line) to the
receiver or transmitter which converts electric power into radio waves, and vice versa. It is usually
used with a radio transmitter or radio receiver. In transmission, a radio transmitter supplies an
oscillating radio frequency electric current to the antenna's terminals, and the antenna radiates the
energy from the current as electromagnetic waves (radio waves). In reception, an antenna intercepts
some of the power of an electromagnetic wave in order to produce a tiny voltage at its terminals,
which is fed to a receiver to be amplified.
Antennas are essential components of all equipment which are used in radio. They are used in
broadcasting systems, broadcast television systems, two-way radio systems, communications
receiver’s systems, radar systems, cell phones systems, and satellite communications systems, garage
door openers systems, wireless microphones systems, Bluetooth enabled devices systems, wireless
computer networks systems, baby monitors systems, and Radio Frequency Identification (RFID) tags
systems on merchandise etc.
7.5.1 Types of antennas
There are a very large variety of antennas used in telecommunication. Here we can discuss at least
four types of antenna among others.
Wire antennas
The wire antennas are dipole, monopole, loop antenna, helix and are usually used in personal
applications, automobiles, buildings, ships, aircrafts and super crafts.
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Fig.7. 12 Wire antenna
Aperture antennas
These are horn antennas and waveguide opening and they are usually used in aircrafts and space
crafts because they are flush-mounted.
Fig.7. 13: A horn antenna with aperture field distribution
Reflector antennas
These are parabolic reflectors and corner reflectors and they are high gain antennas usually used in
radio astronomy, microwave communication and satellite tracking.
Fig.7. 14: Reflector antenna
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4 Array antennas
These are also called Yagi-Uda antennas or micro-strip patch arrays or aperture arrays, slotted
waveguide arrays. They are suitable for very high gain applications with added advantage, such as,
controllable radiation pattern.
Fig.7. 15: Array antenna.
7.5.2 Checking my progress
1. What is meant by an antenna in telecommunication system?
2. State and explain at least two types of antenna
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7.6 BLOCK DIAGRAMS OF TELECOMMUNICATION
Activity 7.6: Investigating communication block
Given the system below, discuss the block of communication system provided in the illustration
below.
Fig.7. 16: Block-diagram of communication system with input and output transducers
Information: Information is any entity or form that resolves uncertainty or provides the answer to a
question of some kind. It is thus related to data and knowledge, as data represents values attributed to
parameters, and knowledge signifies understanding of real things or abstract concepts.
Message: A message is a term standing for information put in an appropriate form for transmission.
Each message contains information. A message can be either analog message (a physical time
variable quantity usually in smooth and continuous form) or a digital message (an ordered sequence
of symbols selected from finite set of elements) as shown in Fg.7.19.
Analog message: a physical time-variable quantity usually in smooth and continuous form.
Digital message: ordered sequence of symbols selected from finite set of elements.
A signal is a mathematical function representing the time variation of a physical variable
characterizing a physical process and which, by using various models, can be mathematically
represented.
In telecommunication, the message is also known as a signal and the signal is transmitted in an
electrical or voltage form. ( i.e Signal ≈ Message)
Fig.7. 17: Analog signal and digital signal representation diagram
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COMPARISON OF AN ANALOG SIGNAL TO A DIGITAL SIGNAL
As discussed in the previous section, we can have the summary of differences between analog signal
and digital signal (see Table 7.2)
Analog Digital
Analog technology records the waveforms
as they are
Digital technology converts analog waveforms
into a set of numbers and records them. The
numbers are converted into voltage streams for
representation
It uses continuous range of values to
represent information
It uses discrete or discontinuous values to
represent information
It can be easily affected by noise (other
unwanted waves)
It is less affected since the noise responses are
analog in nature
The signal is denoted by sine waves The signal is denoted by square waves
The bandwidth is noted in Hertz The bandwidth is noted in bits per second Table 7. 2: Comparison of an analog signal to a digital signal
SOME ELEMENTS OF BLOCK DIAGRAM OF TELECOMMUNICATION
1. Transmission channel which is the electric medium that bridges the distance from source to
destination
2. The receiver to convert the received signal in a form appropriate for the output transducer after
amplifying, filtering, demodulating and decoding it
3. Output transducer to convert the output electrical signal the desired message form
4. Modulation is defined as the process by which some characteristics (i.e. amplitude, frequency,
and phase) of a carrier are varied in accordance with a modulating wave.
5. Encoding is the process of coding the message and changes it in the language understandable by
the transmitter. This operation is realized at the transmitting end
6. Demodulation is the reverse process of modulation, which is used to get back the original
message signal. Modulation is performed at the transmitting end whereas demodulation is
performed at the receiving end
7. Decoding is the reverse process of encoding to retrieve the original message and make it human
understandable message. It is realized at the receiving end
8. Antennas which are aerials used to transmit and receive the signals.
9. The oscillators which are the sources of carrier signals which are used to modulate and help the
original signal to reach the destination
10. The signal normally, must be raised at a level that will permit it to reach its destination. This
operation is accomplished by amplifiers
Fig.7. 18: Block diagram of telecommunication
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7.6.1 Simple radio transmitter
A radio transmitter consists of several elements that work together to generate radio waves that
contain useful information such as audio, video, or digital data. The process by which a radio station
transmits information is outlined in Fig. 7.21.
Fig.7. 19: Block diagram of a radio transmitter
Power supply: Provides the necessary electrical power to operate the transmitter.
The audio (sound) information is changed into an electrical signal of the same frequencies by, say,
a microphone, a laser, or a magnetic read write head. This electrical signal is called an
audio frequency (AF) signal, because the frequencies are in the audio range (20 Hz to
20 000 Hz).
The signal is amplified electronically in AF amplifier and is then mixed with a radio-frequency
(RF) signal called its carrier frequency, which represents that station. AM radio stations have
carrier frequencies from about 530 kHz to 1700 kHz. Today’s digital broadcasting uses the same
frequencies as the pre-2009 analog transmission.
The Modulator or Mixer adds useful information to the carrier wave. The mixing of the audio
and carrier frequencies is done in two ways.
In amplitude modulation (AM), the amplitude of the high-frequency carrier wave is made to
vary in proportion to the amplitude of the audio signal, as shown in Fig.7.3. It is called
“amplitude modulation” because the amplitude of the carrier is altered (“modulate” means to
change or alter).
In frequency modulation (FM), the frequency of the carrier wave is made to change in
proportion to the audio signal’s amplitude, as shown in Fig.7.4. The mixed signal is amplified
further and sent to the transmitting antenna (Fig.7.13.C), where the complex mixture of
frequencies is sent out in the form of EM waves.
Amplifier: Amplifies the modulated carrier wave to increase its power. The more powerful the
amplifier, the more powerful the broadcast.
In digital communication, the signal is put into digital form which modulates the carrier. A television
transmitter works in a similar way, using FM for audio and AM for video; both audio and video
signals are mixed with carrier frequencies.
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7.6.2 Simple radio receiver
A radio receiver is the opposite of a radio transmitter. It uses an antenna to capture radio waves,
processes those waves to extract only those waves that are vibrating at the desired frequency, extracts
the audio signals that were added to those waves, amplifies the audio signals, and finally plays them
on a speaker.
Now let us look at the other end of the process, the reception of radio and TV programs at home. A
simple radio receiver is graphed in Fig. 7.22. The EM waves sent out by all stations are received by
the antenna.
Fig.7. 20 Block diagram of a simple radio receiver
The signal antenna detect and send the radio waves, to the receiver are very small and contain
frequencies from many different stations. The receiver uses a resonant LC circuit to select out a
particular RF frequency (actually a narrow range of frequencies) corresponding to a particular
station.
A simple way of tuning a station is shown in Fig.7.23. When the wire of antenna is exposed to radio
waves, the waves induce a very small alternating current in the antenna.
Fig.7. 21: Simple tuning stage of a radio.
A particular station is “tuned in” by adjusting the capacitance C and/or inductance L so that the
resonant frequency of the circuit equals that of the station’s carrier frequency.
R.F. Amplifier: A sensitive amplifier that amplifies the very weak radio frequency (RF) signal from
the antenna so that the signal can be processed by the tuner.
R.F. Tuner: A circuit that can extract signals of a particular frequency from a mix of signals of
different frequencies. On its own, the antenna captures radio waves of all frequencies and sends them
to the RF amplifier, which dutifully amplifies them all. Unless you want to listen to every radio
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channel at the same time, you need a circuit that can pick out just the signals for the channel you
want to hear. That’s the role of the tuner.
The tuner usually employs the combination of an inductor (for example, a coil) and a capacitor to
form a circuit that resonates at a particular frequency. This frequency, called the resonant frequency,
is determined by the values chosen for the coil and the capacitor. This type of circuit tends to block
any AC signals at a frequency above or below the resonant frequency.
You can adjust the resonant frequency by varying the amount of inductance in the coil or the
capacitance of the capacitor. In simple radio receiver circuits, the tuning is adjusted by varying the
number of turns of wire in the coil. More sophisticated tuners use a variable capacitor (also called a
tuning capacitor) to vary the frequency.
7.6.3 Wireless Radio Communication
Let us now discuss the basic principles of wireless radio communications. We shall mainly
concentrate on the principle of amplitude modulation and demodulation.
The simplest scheme of wireless communication would be to convert the speech or music to be
transmitted to electric signals using a microphone, boost up the power of the signal using amplifiers
and radiate the signal in space with the air of an antenna. This would constitute the transmitter. At
the receiver end, one could have a pick-up antenna feeding the speech or music signal to an amplifier
and a loud speaker. (See Fig.7.24)
Fig.7. 22 Wireless radio communication
The above scheme suffers from the following drawbacks:
(i) EM waves in the frequency range of 20 Hz to 20 kHz (audio-frequency range) cannot be
efficiently radiated and do not propagate well in space.
(ii) Simultaneous transmission of different signals by different transmitters would lead to confusion
at the receiver.
In order to solve these problems; we need to devise methods to convert or translate the audio signals
to the radio-frequency range before transmission and recover the audio-frequency signals back at the
receiver. Different transmitting stations can then be allotted slots in the radio-frequency range and a
single receiver can then tune into these transmitters without confusion. The frequency range 500 kHz
to 20 MHz is reserved for amplitude-modulated broadcast, which is the range covered by most three
band transistor radios. The process of frequency translation at the transmitter is called modulation.
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The process of recovering the audio-signal at the receiver is called demodulation. A simplified block
diagram of such a system is shown in the below figure.
Fig.7. 23 Block diagram of radio transmitter and receiver
7.6.4 Checking my progress
1. What is the importance of power amplifier in simple radio transmitter
2. What do you understand by the following terms
A. Analog message
B. Digital message
3. Draw a circuit diagram of a simple radio receiver
7.7 END UNIT ASSESSMENT
7.7.1 Multiple choices
1. One of the following is used for satellite communication
A. Radio waves C. Microwaves
B. Light waves D. All of these
2. Amplitude –modulated radio waves are received by a tuned radio-frequency ( trf) Receiver. The
receiver has a suitable detector circuit in order to
A. Amplifier the carrier waves
B. Amplifier the audio-frequencies carried
C. Rectifier the carrier waves
D. detect the carrier waves
E. Transfer the audio-frequencies to the radio-frequency amplifier
7.7.2 Structured questions
3. What do you understand by the following terms?
A. Amplifier
B. Modulator
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4. What is meant by telecommunication system?
5. Draw a labeled diagram showing the elements of radio transmitter
7.7.3 Essay question
6. Recently, the government of Rwanda decided to replace analog system of communication by
digital system of communication. Debate about this government policy
7. Explain briefly positive impact of telecommunication in development of a country like Rwanda.
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UNIT 8: NATURE OF PARTICLES AND THEIR INTERACTIONS
Key unit Competence
By the end of the lesson, I should be able to analyse the nature of particle and their interactions
My goals
The key varieties of fundamental subatomic particles and how they were discovered.
Distinguish between fundamental particles and composite particles
Distinguish between particles and antiparticles
Describe how antimatter can be used as a source of energy
State some applications for elementary particles
Compare matter and antimatter
The four ways in which subatomic particles interact with each other.
Analyze the structure of protons, neutrons, and other particles can be explained in terms of
quarks
INTRODUCTORY ACTIVITY
Investigating the elementary particles discovery
In the study of matter description and energy as well as their interactions; the fascinating thing of
discovery is the structure of universe of unknown radius but still to know the origin of matter one
need to know about small and smallest composites of matter. The smallest particle was defined to be
electron, proton, and neutron. But one can ask:
1. Are electron, proton and neutron the only particle that can define the origin of matter?
2. What are other particles matter is composed of?
3. Describe and discuss how particles interact with energy to form matter.
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8.1 ELEMENTARY PARTICLES.
8.1.1 Introduction
Activity 8.1: Investigate the presence of smaller particles
Use internet and retrieve the definition and the information about elementary particles, and then
answer to the following questions.
1. What does elementary particle physics talk about?
2. What are the elementary particles found through your research?
3. Discuss and explain the use of knowledge about the elementary particles.
Particle physics, also known as high-energy physics, is the field of natural science that pursues the
ultimate structure of matter.
The protons and neutrons are collectively called hadrons, were considered as elementary particles
until 1960. We now know that they are composed of more fundamental particles, the quarks.
Electrons remain elementary to this day. Muons and τ-leptons, which were found later, are nothing
but heavy electrons, as far as the present technology can tell, and they are collectively dubbed
leptons. Quarks and leptons are the fundamental building blocks of matter. The microscopic
size that can be explored by modern technology is nearing 10−19 𝑚. The quarks and leptons are
elementary at this level (Nagashima, 2013).
Particle physics is the study of the fundamental constituents of matter and their interactions.
However, which particles are regarded as fundamental have changed with time as physicists’
knowledge has improved. Modern theory called the standard model attempts to explain all the
phenomena of particle physics in terms of the properties and interactions of a small number of
particles of three distinct types (see Fig.8.1):
Two families of fermions (of spin ½): leptons and quarks
One family of bosons (of spin 1)
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Fig.8. 1 Fundamental Standard model of elementary particle
I, II and III represent the first, second and the third generations.
In addition, at least one spin-0 particle, called the Higgs boson, is postulated to explain the origin of
mass within the theory, since without it all the particles in the model are predicted to have zero mass
(see Fig.8.1).
All the particles of the standard model are assumed to be elementary; i.e. they are treated as point
particles, without internal structure or excited states. The most familiar example of a lepton is the
electron 𝑒−(the superscript denotes the electric charge), which is bound in atoms by the
electromagnetic interaction, one of the four fundamental forces of nature. A second well-known
lepton is the electron neutrino, which is a light, neutral particle observed in the decay products of
some unstable nuclei (the so-called β-decays). The force responsible for the β-decay of nuclei is
called the weak interaction.
8.1.2 Checking my progress
1. Particles that make up the family of Hadrons are:
A. baryons and mesons C. Protons and electrons
B. Leptons and baryons D. Muons and Leptons
2. Using the elementary particles, Complete the following sentences
i) One family of bosons of spin 1 called__________which act as ‘force carriers’ in the theory
ii) Two fermions of spin 1/2 called_________and ________
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3. The first antiparticle found was the
A. Positron C. Quark
B. Hyperons D. baryon
4. Explain what is meant by particle physics?
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8.2 CLASSIFICATION OF ELEMENTARY PARTICLES.
Activity 8.2: Classes of elementary particles
Based on the previous introduction section, reread the text and the answer to the following questions.
1. What are the types of elementary particles?
2. What properties are based on to classify elementary particles?
There are three properties that describe an elementary particle ‘’mass,’’ ‘’charge’’ and ‘’spin’’.
Each property is assigned as number value. These properties always stay the same for an elementary
particle.
Mass (m): a particle has mass if it takes energy to increase its speed or to accelerate it. The values
are given in MeV/C2. This comes from special relativity, which tells us that energy equals mass
times the square of the speed of light 𝐸 = 𝑚 × 𝑐2. All particles with mass are affected by gravity
even particles with no mass like photon.
Electric charge (Q): particles may have positive, negative charge or none. If one particle has a
negative charge and another particle has a positive, the two particles are attracted to each other. If
particles have a similar charge, they repel each other. At a short distance this force is much
stronger than the force of gravity which pulls all particles together. An electron has a charge -1
and a proton has a charge +1. A neutron has average charge 0. Normal quarks have charge of 2/3
or -1/3
Spin: the angular momentum or constant turning of particles has a particular value, called its spin
number. Spin for elementary particle is 0, 1 or 1
2. The spin property only donates the presence of
angular momentum.
8.2.1 Classification of particles by mass
The most basic way of classifying particles is by their mass. The heaviest particles are the hadrons
and the lightest one is the leptons.
Fig.8. 2 Particles classification by mass
As seen the diagram above hadrons group is divided into baryons and mesons. Baryons are the
heaviest particles and are followed by mesons.
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Hadrons are composite particles made of quarks held together by the strong force in a similar way as
molecules are held together by electromagnetic force. They are subjected to the strong nuclear force
and are not fundamental particles as they are made up of quarks.
Baryons are composite sub-atomic particle made up of 3 quarks (tri-quarks are distinct from
mesons which are composed of one quark and one antiquark). Baryon comes from Greek word
which means “heavy”. The protons are only stable baryons; all other baryons eventually decay
into proton.
Ex: Protons and neutrons.
Mesons are hadrons sub-atomic particles made up of one quark and one anti-quark bound together
by strong interaction. Ex: Pion and kaon
Each pion has quark and one anti-quark therefore is a meson. It is the lightest meson and generally
the lightest hadrons. They are unstable.
Leptons do not interact via the strong force. They carry electric charge also interact via the weak
nuclear force. They include electron, muons, tau and three the types of neutrino: the electron neutrino
(νE), the muon neutrino (νμ) and the tau neutrino (𝑣𝜏).
In summary, leptons are subjected to the weak nuclear force and they do not feel the strong nuclear
force.
Examples: Electron, muons and neutrino.
8.2.2 Classification of particles by spin.
The spin classification determines the nature of energy distribution in a collection of particles.
Particles of integer spin obey Bose-Einstein statistics whereas those of half-integer spin behave
according to Fermi-Dirac statistics as shown in the following chart
210
All fundamental particles are classified into fermions and bosons. Fermions have half-integer spin
while bosons have full integer spin. Electrons and nucleons are fermions with spin ½. The
fundamental bosons have mostly spin 1. This includes the photon. The pion has spin 0, while the
graviton has spin 2. There are also three particles, the W+, W− and Z0 bosons, which are spin
1. They are the carriers of the weak interactions.
Fermions are particles which have half-integer spin and therefore are constrained by the Pauli
Exclusion Principle (see Section 8.4). It includes electrons, protons and neutrons.
The fact that electrons are fermions is foundational to the buildup of the periodic table of elements
since there can be only one electron for each state in an atom (only one electron for each possible set
of quantum numbers). The fermion nature of electrons also governs the behavior of electrons in a
metal where at low temperatures all the low energy states are filled up to a level called the Fermi
energy. This filling of states is described by Fermi-Dirac statistics.
8.2.3 Checking my progress
1. How can elementary particles be classified?
2. Elementary particles which are made up of one quark and one anti-quark are called
A. AProtons C. baryons .
B. neutrons D. mesons E. Leptons
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3. The Sub-atomic particle made up of 3 quarks are called
A. Leptons C. kaon
B. Pion D. Baryons
4. What do you understand by the term elementary particle? .
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8.3 ANTI PARTICLE AND PAULI’S EXCLUSION PRINCIPLE
8.3.1 Concept of particle and antiparticle
Activity 8.3:
Discuss the following terms:
1. Particle
2. Antiparticle
There are two important points about pair production. The first is that you need to collect energy to
produce the electron-positron pair. You need the equivalent rest mass of energy that is the amount of
energy contained in the both particle and anti-particle when at rest. The energy converted to mass is
‘lost’ or fully ‘’bound’’ until the particle is annihilated and the energy can be recovered. The second
thing is that it needs a correct environment. The process does not occur unless certain conditions are
present.
Viewing the phenomena as a creative process we can say a threshold amount of energy is sacrificed
in a correct context to manifest a pair of particle with a physical mass. It can be said something was
created out of nothing. That is before the interaction, no particles with mass existed. After
interaction, there were two particles with mass. Hence something was created out of nothing. But this
can be said only because of the perspective taken when viewing the process.
For every charged particle of nature, whether it is one of the elementary particles of the
standard model, or a hadron, there is an associated particle of the same mass, but opposite
charge, called its antiparticle. This result is a necessary consequence of combining special relativity
with quantum mechanics. This important theoretical prediction was made by Dirac and follows from
the solutions of the equation he first wrote down to describe relativistic electrons
8.3.2 Pauli’s exclusion principle,
Pauli’s exclusion principle is a quantum mechanical principle which states that:
“Two or more identical fermions (particles with half-integer spin) cannot occupy the same
quantum state simultaneously.”
In case of electrons in atoms it can be stated as follows: it is impossible for two electrons of a poly-
electron atom to have the same values of the four quantum numbers:
The principle quantum number (n), the angular momentum quantum number (l), the magnetic
quantum number (ml) and the spin quantum number (ms).
For example, if two electrons reside in the same orbital and if their ms must be different and thus
like electrons must have opposite half integer spin projections of 1
2and −
1
2. This principle was
formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all
fermions with his spin–statistics theorem of 1940.
213
Particles with an integer spin, or bosons, are not subject to the Pauli Exclusion Principle: any number
of identical bosons can occupy the same quantum state, for instance, photons produced by
a laser and Bose–Einstein condensate.
The Pauli Exclusion Principle describes the behavior of all fermions (particles with "half-
integer spin"), while bosons (particles with "integer spin") are subject to other principles. Fermions
include elementary particles such as quarks, electrons and neutrinos. Additionally, baryons such
as protons and neutrons (subatomic particles composed from three quarks) and some atoms (such
as helium-3) are fermions, and are therefore described by the Pauli Exclusion Principle as well.
8.3.3 Checking my progress
1. What do you understand by antiparticle?
2. State Pauli’s exclusion principle?
3. Why Pauli’s exclusion Principle is known as exclusion?
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8.4 FUNDAMENTAL INTERACTIONS BY PARTICLE EXCHANGE
Activity 8.4 Fundamental interaction
Using internet, discusses the fundamental interactions in terms of exchange particles, then find the
relation between the following concepts.
1. Gravitational forces
2. electroweak force,
3. Strong force and
4. Weak forces.
8.4.1 Forces and Interactions
Physicists have recognized three basic forces:
- The gravitational force is an inherent attraction between two masses. Gravitational force is
responsible for the motion of the planets and Stars in the Universe. It is carried by Graviton. By
Newton’s law of gravitation, the gravitational force is directly proportional to the product of the
masses and inversely proportional to the square of the distance between them. Gravitational force
is the weakest force among the fundamental forces of nature but has the greatest large−scale
impact on the universe. Unlike the other forces, gravity works universally on all matter and
energy, and is universally attractive
- The electric force is a force between charges
- The magnetic force, which is a force between magnets or between magnetic body and
ferromagnetic body.
In the 1860s, the Scottish physicist James Clerk Maxwell developed a theory that unified the electric
and magnetic forces into a single electromagnetic force. Maxwell's electromagnetic force was soon
found to be the "glue" holding atoms, molecules, and solids together. It is the force between charged
particles such as the force between two electrons, or the force between two current carrying wires. It
is attractive for unlike charges and repulsive for like charges. The electromagnetic force obeys
inverse square law. It is very strong compared to the gravitational force. It is the combination of
electrostatic and magnetic forces.
The discovery of the atomic nucleus, about 1910, presented difficulties that could not be explained
by either gravitational or electromagnetic forces. The atomic nucleus is an unimaginably dense ball
of protons and neutrons. But what holds it together against the repulsive electric forces between the
protons? There must be an attractive force inside the nucleus that is stronger than the repulsive
electric force. This force, called the strong force, is the force that holds the protons and neutrons
together in the nucleus of an atom. It is the strongest of all the basic forces of nature. It, however, has
the shortest range, of the order of 10−15 m. This force only acts on quarks. It binds quarks together to
form baryons and mesons such as protons and neutrons. The strong force is mediated or carried by
Gluons. Quarks carry electric charge so they experience electric and magnetic forces.
In the 1939, physicists found that the nuclear radioactivity called beta decay could not be explained
by either the electromagnetic or the strong force. Careful experiments established that the decay is
due to a previously undiscovered force within the nucleus. The strength of this force is less than
either the strong force or the electromagnetic force, so this new force was named the weak force.
215
Weak nuclear force is important in certain types of nuclear process such as β-decay. This force is not
as weak as the gravitational force. The weak force acts on both leptons and quarks (and hence on all
hadrons). The weak force is carried by W+, W- and Z. Leptons – the electrons, muons and tau – are
charged so they experience electric and magnetic forces.
Of these, our everyday world is controlled by gravity and electromagnetism. The strong force binds
quarks together and holds nucleons (protons & neutrons) in nuclei.
The weak force is responsible for the radioactive decay of unstable nuclei and for interactions of
neutrinos and other leptons with matter.
By 1940, the recognized forces of nature (fundamental forces) were four:
gravitational forces between masses,
electromagnetic forces resulting from the combination of electric and magnetic fields,
strong force (nuclear force) between subatomic particles,
weak forces that arise in certain radioactive decay processes.
By 1980, Sheldon Glashow, Abdus Salam, and Steven Berg developed a theory that unifies
electromagnetism and weak force into electroweak force. Hence, our understanding of the forces of
nature is in terms of three fundamental forces:
the gravitational force,
the electroweak force,
the strong force.
The Table 8.1 below summaries the fundamental forces and force carriers.
Force Carriers Symbol charge Mass
Electromagnetic Photon 𝛾 0 0
Strong Gluon 𝑔 0 0
Weak W boson 𝑊+
𝑊−
+
-
80.1 GeV
80.6 GeV
Z boson 𝑍 0 91.2 GeV
Gravitational Graviton 𝐺 0 0 Table 8. 1 Forces and their carriers
W boson: short-lived elementary particle; one of the carriers of the weak nuclear force
Z boson: short-lived elementary particle; one of the carriers of the weak nuclear force
Graviton: the hypothetical particle predicted to carry the gravitational force
All the forces of nature should be capable of being described by single theory. But only at high
energies should be the behavior of the forces combines, this is called unification.
We can compare the relative strengths of the electromagnetic repulsion and the gravitational
attraction between two protons of unit charge using the above equations.
Force Relative Gauge Boson Mass (relative Charge Spin
216
strength to proton)
Strong 1 Gluon (g) 0 0 1
Electromagnetic 1
137
Photon (𝛾) 0 0 1
Weak 10−9 𝑊±, 𝑍 86, 97 ±1, 0 1
Gravity 10−38 Graviton (G) 0 0 2 Table 8. 2 Forces and their quanta, the gauge bosons and charge in units of electron charge.
1. The 2 up quarks (u) in a proton are separated by a distance . These quarks each
have an electric charge , and mass of kgmu
30107 so they repel each other through an
electric force obeying Coulomb’s law. They also attract each other through a gravitational force.
What is the ratio of the magnitude of the electric and gravitational forces between these 2 quarks?
Gravitational force:2r
mmGF uu
gr
Electric force:
Divided by :
𝐹𝑔𝑟
𝐹𝑒𝑙=
𝐺
𝑘 𝑚𝑢𝑚𝑢
𝑞𝑢𝑞𝑢=
9𝐺𝑚2
4𝑘𝑒2=
9 (6.67𝑥10−11 𝑁.𝑚2
𝑘𝑔2) (7𝑥10−30𝑘𝑔)2
4(8.99𝑥 109𝑁.𝑚2
𝐶2 )(1.6𝑥10−19𝐶)2= 3𝑥10−41
Thus the gravitational is the weakest of the fundamental forces.
These interactions and their relative strengths are summarized in Table 8.1
n
8.4.2 Checking my progress
1. Particles that interact by the strong force are called:
A. Leptons C. Muons
B. hadrons D. Electrons
2. Name the four fundamental interaction and the particles that mediate each interaction.
mr 15101
e3
2
2r
qqkF uu
el
Example 8.1
217
8.5 UNCERTAINTY PRINCIPLE AND PARTICLE CREATION
8.5.1 The concept of uncertainty principle
Activity 8.5: Investigation of particle creation and position.
Basing on the knowledge and skills obtained from the previous sections of this unit, use internet to
find the meaning of the particle creation.
- Is it possible to know the exact location of an elementary particle?
- Discuss and explain your findings.
The discovery of the dual wave–particle nature of matter forces us to re-evaluate the kinematic
language we use to describe the position and motion of a particle.
In classical Newtonian mechanics we think of a particle as a point. We can describe its location and
state of motion at any instant with three spatial coordinates and three components of velocity. But
because matter also has a wave aspect, when we look at the behaviour on a small enough scale
comparable to the de Broglie wavelength of the particle we can no longer use the Newtonian
description. Certainly no Newtonian particle would undergo diffraction like electrons do.
To demonstrate just how non Newtonian the behaviour of matter can be, let’s look at an experiment
involving the two-slit interference of electrons (Fig.8.4).
We aim an electron beam at two parallel slits, just as we did for light. (The electron experiment has
to be done in vacuum so that the electrons don’t collide with air molecules.)
Fig.8. 3Experiment involving the two-slit interference of electrons
What kind of pattern appears on the detector on the other side of the slits?
218
The answer is: exactly the same kind of interference pattern we saw for photons. Moreover, the
principle of complementarily, tells us that we cannot apply the wave and particle models
simultaneously to describe any single element of this experiment. Thus we cannot predict exactly
where in the pattern (a wave phenomenon) any individual electron (a particle) will land. We can’t
even ask which slit an individual electron passes through. If we tried to look at where the electrons
were going by shining a light on them that is, by scattering photons off them the electrons would
recoil, which would modify their motions so that the two-slit interference pattern would not appear.
Just as electrons and photons show the same behaviour in a two-slit interference experiment,
electrons and other forms of matter obey the same Heisenberg uncertainty principles as photons do:
Heisenberg uncertainty principle for position and momentum is given by
(∆𝑥)(∆𝑝𝑥) ≥ℎ
4𝜋 (8.03)
This is a mathematical statement of the Heisenberg uncertainty principle
Or it is sometimes called, the indeterminacy principle. It tells us that we cannot measure both the
position and momentum of an object precisely at the same time.
The uncertainty principle relates energy and time, examining this as follows. The object to be
detected has an uncertainty in position ∆𝑥 ≈ 𝜆. the photon that detects it travels with speed c, and it
takes a time Δ𝑡 ≈∆𝑥
𝐶≈
𝜆
𝐶 to pass through the distance of uncertainty.
Hence, the measured time when our object is at given position is uncertain by about ∆𝑡 =𝜆
𝐶 since the
photon can transfer some or all of energy
𝐸 = ℎ𝑓 =ℎ𝑐
𝜆 To our object, the uncertainty in energy of our object as result is Δ𝐸 ≈
ℎ𝑐
𝜆
The product of these two uncertainties is (ΔΕ)(Δ𝑡) ≈ ℎ . A more careful calculation gives
(ΔΕ)(Δ𝑡) ≥ℎ
4𝜋 (8.04)
The quantity ℎ
2𝜋 appears so often in quantum mechanics that for convenience is given the symbol ℏ
(“h-bar”).
ℏ =ℎ
2𝜋=
6.626×1𝑜−34𝐽.𝑠
2𝜋= 1.055 × 10−34𝐽. 𝑠.
Thus (Δx)(Δ𝑝𝑥) ≥ℏ
2 and (ΔΕ)(Δ𝑡) ≥
ℏ
2 (8.05)
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8.5.2 Checking my progress
1. The idea of uncertainty is used in many contexts; social, economic and scientific. People often
talk about uncertain times, and when you perform a measurement you should always estimate the
uncertainty (sometimes called the error). In physics the Heisenberg Uncertainty relation has a very
specific meaning.
a. Write down the Heisenberg uncertainty relation for position and momentum.
b. Explain its physical significance.
c. Does the Heisenberg uncertainty principle need to be considered when calculating the
uncertainties in a typical first year physics experiment? Why or why not?
d. Discuss the following statement: the uncertainty principle places a limit on the accuracy with
which a measurement can be made. Do you agree or disagree, and why?
2. An electron is confined within a region of width 5 × 10−11𝑚 (Roughly the Bohr radius)
a) Estimate the minimum uncertainty in the component of the electron’s momentum.
b) What is the kinetic energy of an electron with this magnitude of momentum? Express
your answer in both joules and electron volts.
220
8.6 MATTER AND ANTIMATTER (PAIR PRODUCTION AND
ANNIHILATION)
Activity 8.6: Describing the matter and antimatter
Use internet to describe the following concepts:
1. matter and give examples of matter particles
2. antimatter and give examples of antimatter particles
3. Pair production
4. Annihilation
8.6. 1 Introduction
Matter is a substance that has mass and takes up a space by having a volume. This include atoms and
anything made up of these but no other energy phenomena or wave such as light or sound.
Everything around you is made up of matter and is composed of particles including the fundamental
fermions (quarks, leptons, antiquarks and antileptons) which generally are matter particles and
antimatter particles.
Antimatter is a material composed of the antiparticle to the corresponding particle or ordinary
particles. In theory a particle and its antiparticle have the same mass as one another but opposite
electric charge and other differences in quantum numbers.
Neutrons have antineutrons, electrons have positrons and neutrons have antineutrons as their
respective antimatter. It was once thought that matter would neither be created nor destroyed. We
know that energy and mass are interchangeable.
8.6.2 Pair production and annihilation
Pair production is a crucial example that photon energy can convert into kinetic energy as well as
rest mass energy. Schematic diagram about the process of pair production is shown in Fig.8.5. The
high-energy photon that has energy hf loses its entire energy when it collides with nucleus. Then, it
makes pair of electron and positron and gives kinetic energy to each particle.
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Fig.8. 5 Schematic diagram about the process of pair production
Annihilation: When a particle collides with its antiparticle, the two annihilate each other with their
mass being entirely converted into energy by the process called ‘’Annihilation’’
These particles and anti-particles can meet each other and annihilate one another (See Fig.8.6). . In
each case the particle and its antiparticle annihilate each other, releasing a pair of high energy gamma
photons
Fig.8. 4: Annihilation process during pair-production.
In this example, a proton and an anti-proton meet each other and annihilate, producing high energy
gamma rays in the form of photons. Rest mass, charge, momentum and energy are conserved.
They can also be produced from a high energy photon, this is called pair production.
8.6.3 Application of antimatter
Antimatter as a form of antiparticle of sub atomic particles has a variety of applications:
Positron emission tomography can be used to potentially treat cancer.
Stored antimatter can be used for interplanetary and inter stellar travel.
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Antimatter reactions have practical applications in medical energy.
Antimatter has been considered as a trigger mechanism for nuclear weapons because whenever
antimatter meets its corresponding matter the energy is released by annihilation.
8.6.4 Checking my progress
1. Antimatter as a form of____________of sub atomic particles
a) Electron b) proton c) matter d) antiparticle e) none of them is correct
2. b) The process in which a particle and antiparticle unite annihilate each other and produce one
or more photons is called………
3. What happens when matter and antimatter collide?
4. Compare matter and antimatter
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8.7 END UNIT ASSESSMENT
8.7.1 Multiple choices
1. The positron is called the antiparticle of electron, because it
A. Has opposite charge and Annihilates with an electron
B. Has the same mass
C. Collides with an electron
D. Annihilates with an electro
2. Beta particles are
A. Neutrons
B. Protons
C. Electrons
D. Thermal neutrons
3. If gravity is the weakest force, why is it the one we notice most?
A. Our bodies are not sensitive to the other forces.
B. The other forces act only within atoms and therefore have no effect on us.
C. Gravity may be “very weak” but always attractive, and the Earth has enormous mass. The strong
and weak nuclear forces have very short range. The electromagnetic force has a long range, but
most matter is electrically neutral.
D. At long distances, the gravitational force is actually stronger than the other forces.
E. The other forces act only on elementary particles, not on objects our size.
8.7.2 Structured questions
4. According to the classification of elementary particles by mass. Complete the following figure
5. (a) (i) State two differences between a proton and a positron.
(ii) A narrow beam of protons and positrons travelling at the same speed enters a uniform magnetic
field. The path of the positrons through the field is shown in Fig.8.7. Sketch on this figurethe path
you would expect the protons to take.
224
Fig.8. 5 Particles in magnetic field
(iii) Explain why protons take a different path to that of the positrons.
6. A positron with kinetic energy 2.2 MeV and an electron at rest annihilate each other. Calculate the
average energy of each of the two gamma photons produced as a result of this annihilation.
8.7.3 Essay question
7. Describe briefly the following particle-terms terms: 𝜋-meson, muon, neutrino,
antiparticle, hadrons and lepton.
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UNIT 9: PROPERTIES AND BASIC PRINCIPLES OF QUARKS.
The standard model of elementary particles
Key unit Competence
By the end of this unit, I should be able to organize the properties and basic principles of quarks.
My goals
- List types of quarks, identify quarks, antiquarks and hadrons (baryons and mesons)
- Define baryon number and state the law of conservation of baryon number.
- Interpret the baryon number and apply the law of conservation of baryon number
- State colors of quarks and gluons.
- Explain how color forms bound states of quarks.
- Formulate the spin structure of hadrons (baryon and mesons)
INTRODUCTORY ACTIVITY
In the study of matter description and energy as well as their interactions; the fascinating thing of
discovery is the structure of universe of infinite size but still there is a task to know the origin of
matter. The smallest particle was defined to be electron, proton, and neutron. But one can ask:
1. What particles are components of matter?
2. Describe and discuss how particles interact with energy to form matter.
9.1 INTRODUCTION
Activity 9.1: Investigating about elementary particles
226
Considering the knowledge and skills obtained from unit 8, about the study of elementary particles,
discuss and explain the following questions:
1. Discuss the major groups of elementary particles
2. Explain and analyze the family of quarks and their interactions.
3. Why should we learn about elementary particles?
Particle physics is the field of natural science that pursues the ultimate structure of matter. This is
possible in two ways. One is to look for elementary particles, the ultimate constituents of matter at
their smallest scale, and the other is to clarify what interactions are acting among them to construct
matter as we see them. The exploitable size of microscopic objects becomes smaller as technology
develops. What was regarded as an elementary particle at one time is recognized as a structured
object and relinquishes the title of “elementary particle” to more fundamental particles in the next
era. This process has been repeated many times throughout the history of science (Nagashima, 2013).
In the 19th century, when modern atomic theory was established, the exploitable size of the
microscopic object was ~10−10𝑚 and the atom was “the elementary particle”. Then it was
recognized as a structured object when J.J. Thomson extracted electrons in 1897 from matter in the
form of cathode rays. Its real structure (the Rutherford model) was clarified by investigating the
scattering pattern of α-particles striking a golden foil (See Fig.9.1).
Fig.9. 1: Scattering pattern of α-particles striking a golden foil.
In 1932, Chadwick discovered that the nucleus, the core of the atom, consisted of protons and
neutrons. In the same year, Lawrence constructed the first cyclotron. In 1934 Fermi proposed a
theory of weak interactions. In 1935 Yukawa proposed the meson theory to explain the nuclear force
acting among them.
It is probably fair to say that the modern history of elementary particles began around this time. The
protons and neutrons together with their companion pions, which are collectively called hadrons,
were considered as elementary particles until 1960. We now know that they are composed of more
fundamental particles, the quarks. Electrons remain elementary to this day. Muons and τ-leptons,
which were found later, are nothing but heavy electrons, as far as the present technology can tell, and
they are collectively dubbed leptons. Quarks and leptons are the fundamental building blocks of
227
matter. The microscopic size that can be explored by modern technology is nearing 10−19 𝑚. The
quarks and leptons are elementary at this level (Nagashima, 2013). Some composite particles as
stated by (Hirsch, 2002) are summarized in the tables below
9.1.2 Checking my progress
1. Each hadron consists of a proper combination of a few elementary components called
A. photons. C. quarks.
B. vector bosons. D. meson-baryon pairs.
2. Which of the following is not conserved in a nuclear reaction?
A. nucleon number. C. charge
B. baryon number. D. All of the above are conserved.
3. The first antiparticle found was the
A. positron. C. quark.
B. hyperon. D. baryon.
4. The proton, neutron, electron, and the photon are called
A. secondary particles. C. basic particles.
B. fundamental particles. D. initial particles.
5. The exchange particle of the electromagnetic force is the
A. gluon. C. proton.
B. muon. D. photon.
6. Particles that are bound by the strong force are called
A. leptons. C. muons.
B. hadrons. D. electrons.
7. At the present time, the elementary particles are considered to be the
A. photons and baryons. C. baryons and quarks.
B. Leptons, quarks and bosons D. baryons and leptons.
8. The electron and muon are both
A. hadrons. C. baryons.
B. leptons. D. mesons.
9. Particles that make up the family of hadrons are
A. baryons and mesons. C. protons and electrons.
228
B. leptons and baryons. D. muons and leptons.
10. Is it possible for a particle to be both:
A. A lepton and a baryon? C. A meson and a quark?
B. A baryon and hadron? D. A hadron and a lepton?
11. Distinguish between
a) fermions and bosons
b) leptons and hadrons
c) mesons and baryon number
12. Which of the four interactions (strong, electromagnetic, weak, gravitational) does an electron,
neutrino, proton take part in?
229
9.2 TYPES OF QUARKS
Activity 9.2: Investigating quark particles
Use search internet and find the explanation about quarks and types of quarks
A quark is a type of elementary particle and a fundamental constituent of matter. Quarks combine to
form composite particles called hadrons, the most stable of which are protons and neutrons, the
components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never
directly observed or found in isolation; they can be found only within hadrons, such as baryons (of
which protons and neutrons are examples) and mesons. For this reason, much of what is known
about quarks has been drawn from observations of the hadrons themselves (Douglass, PHYSICS,
Principles with applications., 2014).
Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin.
Quarks are the only elementary particles in the Standard Model of particle physics to experience all
four fundamental interactions, also known as fundamental forces (electromagnetism, gravitation,
strong interaction, and weak interaction (see section 8.5), as well as the only known particles whose
electric charges are not integer multiples of the elementary charge.
There are six types of quarks, known as flavors: up, down, strange, charm, top, and bottom (see
Fig. 9.2). Up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly
change into up and down quarks through a process of particle decay (the transformation from a
higher mass state to a lower mass state). Because of this, up and down quarks are generally stable
and the most common in the universe, whereas strange, charm, bottom, and top quarks can only be
produced in high energy collisions (such as those involving cosmic rays and in particle accelerators).
For every quark flavor there is a corresponding type of antiparticle, known as an antiquark, that
differs from the quark only in that some of its properties have equal magnitude but opposite sign
(Nagashima, 2013).
Fig.9. 2 Types of quarks
230
Checking my progress
1. A proton is made up of
A. one up quark and two down quarks C. two up quarks and a down quark
B. an up quark and down antiquark D. strange quark and an anti-strange quark
2. Particles that are un affected by strong nuclear force are
A. protons C. neutrons
B. leptons D. bosons
3. Particle which explains about mass of matter is called
A. Higgs boson C. leptons
B. Protons D. neutrons
4. Describe the types and the characteristics of the quarks as well as their interaction properties.
231
9.3 BARYON NUMBER, LEPTON NUMBER AND THEIR LAWS OF
CONSERVATION
Activity 9.3: Investigating about particle numbers.
Use search internet and retrieve the meaning of the following property of elementary particles.
- Baryon numbers and
- Lepton numbers
One of the important uses of high energy accelerators is to study the interactions of elementary
particles with each other. As a means of ordering this sub-nuclear world, the conservation laws are
indispensable. The law of conservation of energy, of momentum, of angular momentum, and of
electric charge is found to hold precisely in all particle interactions.
A study of particle interactions has revealed a number of new conservation laws which (just like the
old ones) are ordering principles. They help to explain why some reactions occur and others do not.
For example, the following reactions have never been found to occur:
𝑝 + 𝑛 ↛ 𝑝 + 𝑝 + �̅� (9.01)
Even though charge, energy, and so on are conserved (�̅� means an antiproton and ↛ means the
reaction does not occur). To understand why such a reaction does not occur, physicists hypothesized
a new conservation law, the conservation of baryon number.
Thus the law of conservation of baryon number states that: “Whenever a nuclear reaction or decay
occurs, the sum of baryon numbers before the process must equal the sum of the baryon numbers
after the process.”
Baryon number is a generalization of nucleon number, which is conserved in nuclear reaction and
decays. All nucleons are defined to have baryon number 𝐵 = +1, and all antinucleons (antiprotons,
antineutrons) have 𝐵 = −1. All other types of particles, such as photons, mesons, and electrons and
other leptons have 𝐵 = 0.
The reaction (9.01) shown above does not conserve baryon number since the left side 211 B
, and the right-hand side has 1111 B .
On the other hand, the following reaction does conserve B and does occur if the incoming proton has
sufficient energy
pppppp (9.02)
2111111 B
As indicated, 𝐵 = +2 on both sides of this equation. From these and other reactions, the
conservation of baryon number has been established as basic principle of physics.
232
Also useful are the conservation laws of the three lepton numbers, associated with weak interactions
including decays, in ordinary 𝛽 decay, an electron or positron is emitted along with a neutrino or
antineutrino. In a similar type of decay, a particle known as 𝜇 or mu meson, or muon, can be emitted
instead of an electron. The muon seems to be much like an electron, except its mass is 207 times
larger ( 2/106 cMeV ). The neutrino e that accompanies an emitted electron is found to be different
from the neutrino that accompanies an emitted muon. Each of these neutrinos has an antiparticle
�̅�𝑒 𝑎𝑛𝑑 �̅�𝜇.
The law of conservation of electron-lepton number states that: “The sum of the electron-lepton
numbers before reaction or decay must equal the sum of the electron-lepton numbers after the
reaction or decay.”
In ordinary 𝛽 decay we have for example, eepn , a second quantum number, muon lepton
number L , is conserved. The and are assigned 1L and and have 1L
, whereas other particles have 0L , L too is conserved in interaction and decays. Similarly
assignment can be made for the tau lepton number associated with the Lepton and its neutrino,
.
Keep in mind that antiparticles have not only opposite electric charge from their particles, but also
opposite B, Le, L
m and L
. For example, neutrino has 1B , an antineutrion has 1B while all the
𝐿′𝑠 𝑎𝑟𝑒 𝑧𝑒𝑟𝑜.
Example 9.1:
1.Which of the following decay is possible for muon decay:
(a) veu
(b) ueu
(c) eveu
These particles have 0L
Answer:
Au has 1L and 0eL . This is the initial state, and the final state (after decay) must also
have 1L , 0eL
(a) The final state has 000 L and 011 eL would not be conserved and indeed this
decay is not observed to occur.
(b) The final state of reaction has 01100 L and 0011 eL so both L and eL
are conserved. This is in fact the most common decay mode of the .
(c) The reaction does not occur because 2eL in the final state) is not conserved, nor L
233
The particle predicted by Yukawa was discovered in cosmic rays by C.F Powell and G. Ochialini in
1947, and is called the or pi meson, or simple called pion.
It comes in three states: , or 0 . The 𝜋+ and 𝜋− have mass of 139.6 𝑀𝑒𝑉/𝑐2 and the 𝜋0 has a
mass of 2/0.135 cMeV , all close to Yukawa’s prediction (Douglass, PHYSICS, Principles with
applications., 2014). All three interact strongly with matter.
Reactions observed in the laboratory, using a particle accelerator, include:
0 pppp (9.03)
nppp (9.04)
The incident proton from the accelerator must have sufficient energy to produce the additional mass
of the free pion. Baryon number conservation keeps the proton stable, since it forbids the decay of
the proton to e.g. a 0 and a each of which have baryon number of zero.
Checking my progress
1. Discuss and explain the law of conservation of baryon numbers and give an example.
2. Discuss whether the following reaction obeys the conservation of baryon number:
a. npppp
b. nppp
234
9.5 SPIN STRUCTURES OF HADRONS (HADRONS AND MESONS)
Activity 9.5: Investigating the structure of elementary particles
Use search internet and find the structure of elementary particles: Hadrons and mesons.
Discuss and explain your findings in a brief summary about structure of hadrons.
There are hundreds of hadrons, on the other hand, and experiments indicate they do have an internal
structure. In 1963, M. Gell-Mann and G. Zweig proposed that none of the hadrons, not even the
proton and neutron, are more fundamental, point like entities called, somewhat whimsically, quarks.
Today, the quark theory is well accepted, and quarks are considered the truly elementary particles,
like leptons. The three quarks originally proposed we labeled u, d, s and have the names up, down
and strange. The theory today has six quarks, just as there are six leptons based on presumed
symmetry in nature,
The other three quarks are called charmed, bottom and top (see Fig.9.2). The theory names apply
also to new properties of each (quantum numbers c, t, b) that distinguish the new quarks from the old
quarks (see Table 9.1 below), and which (like strangeness) are conserved in strong, but not weak,
interactions. All quarks have spin1
2 and an electric charge of either e
3
2 or e
3
1 (that is, a fraction of
the previously thought smallest charge e). Antiquarks have opposite sign of electric charge Q, baryon
number B, strangeness S, charm c, bottomness b, and topness t.
Quarks
Name Symbol Charge Q Baryon
number B
Strangeness
S
Charm c Bottomnes
b
TopnessT
Up U e
3
2
3
1
0 0 0 0
Down D e
3
1
3
1
0 0 0 0
Strange S e
3
1
3
1
1 0 0 0
Charmed C e
3
2
3
1
0 1 0 0
Bottom B e
3
1
3
1
0 0 1 0
Top T e
3
2
3
1
0 0 0 1
Table 9. 1 Properties of Quarks (Antiquarks have opposite sign Q, B. S, c, b and t
All hadrons are considered to be made up of combinations of quarks, and their properties are
described by looking at their quark content. Mesons consist of quark-antiquark pair (See Table 9.2).
For example, a meson is a du combination: note that for the du pair,
235
eeeQ 13
1
3
2
03
1
3
1B
000 S
as they must for a 𝜋+; and a 𝐾+ = 𝑢�̅�, with 𝑄 = +1, 𝐵 = 0, 𝑆 = +1. Baryons, on other hand,
consist of three quarks. For example, a neutron is 𝑛 = 𝑑𝑑𝑢, whereas an antiproton �̅� = �̅��̅��̅� (see
Table 9.3). Strange particles all contain an s or �̅� quark, whereas charmed particles contain a c or 𝑐̅ quarks. From Table 9.2 and Table 9.3, you will find that:
𝑀𝒆𝒔𝒐𝒏 = 𝒒𝒖𝒂𝒓𝒌 + 𝒂𝒏𝒕𝒊𝒒𝒖𝒂𝒓𝒌
𝑩𝒂𝒓𝒚𝒐𝒏 = 𝟑 𝒒𝒖𝒂𝒓𝒌𝒔
Some examples of mesons, with their quark compostions and the corresponding values of their
electric charge Q, strangeness S, charm C and bottom �̃�
Particle Q S C �̃�
π+ ud̅ 1 0 0 0
K− su̅ −1 −1 0 0
D− dc̅ −1 0 −1 0
D+ cs̅ 1 1 1 0
B− bu̅ −1 0 0 −1
Γ bb̅ 0 0 0 0 Table 9. 2 Properties of some mesons
Some of examples of baryons, with their quark compositions and the corresponding values of their
electric charge Q, Strangeness S, charm C and bottom B̃
Particle Q S C �̃�
𝐩 𝐮𝐮𝐝 𝟏 𝟎 𝟎 𝟎
𝐧 𝐮𝐝𝐝 𝟎 𝟎 𝟎 𝟎
𝚲 𝐮𝐝𝐬 𝟎 −𝟏 𝟎 𝟎
𝚲𝐜 𝐮𝐝𝐜 𝟏 𝟎 𝟏 𝟎
𝚲𝐛 𝐮𝐝𝐛 𝟎 𝟎 𝟎 −𝟏 Table 9. 3 Properties of some baryons
After the quark theory was proposed, physicists began looking for those fractionally charged
particles, but direct detection has not been successful. Current models suggest that quarks may be so
tightly bound together that they may not ever exist singly in the free State.
236
But observations of very high energy electrons scattered off protons suggest that protons are indeed
made up of constituents.
Today, the truly elementary particles are considered to be the six quarks, the six leptons and the
gauge bosons that carry the fundamental forces. See Table 9.4 where the quarks and leptons are
arranged in three “generations.” Ordinary matter-atoms made of protons, neutrons, and electrons are
contained in the “first generation”. The others are thought to have existed in the very early universe,
but are seen by us today at powerful accelerators or in cosmic rays. All of the hundreds of hadrons
can be accounted for by combinations of the six quarks and six antiquarks.
Gauge
bosons
Force First
generation
Second
generation
Third
generation
Gluons Strong Quarks 𝑢, 𝑑 𝑠, 𝑐 𝑏, 𝑡
𝑊±, 𝑍0 Weak Leptons 𝑒, 𝑣𝑒 𝜇, 𝜈𝜇 𝜏, 𝜈𝜏
𝛾 (𝑝ℎ𝑜𝑡𝑜𝑛) EM Table 9. 4 The Elementary Particles as seen nowadays
Note that the quarks and leptons are arranged into three generations each.
1.Find the baryon number, charge, and strangeness for the following quark combinations, and
identify the hadrons particle that is made up of these quark combinations:
(a)udd , (b) uu , (c) uss , (d) sdd and (e) bu
Answer:
We use Table 9.1, Table 9.2 and Table 9.3 to get the properties of the quarks, then to find the
particle that has these properties.
a. udd has 03
1
3
2 eeQ , 1
3
1
3
1
3
1B , 0000 S , as well as 0c ,
bottomness 0 and topness 0 .
The only baryon (baryonic number =+1) with 0Q , 0S etc, is the neutron (Table 9. 3)
b. uu has 03
1
3
2 eeQ , 0B and all other quantum numbers = 0. It sounds like a 0 ( dd
also gives a 0 and we say a 0 is dduu ).
c. uss has 0Q , 1B , 2S , others 0 . This is 0 .
d. sdd has 1Q , 1B , 1S , so must be a
e. ub has 1Q , 0B , 0S , 0C , bottomness 1 and topness 0 . This must be a B
meson.
Checking may progress
1. Identify the particle corresponding to each of the following quark combinations:
Example 9.1
237
a. su̅
b. du̅
c. uds
d. uus
2. The 𝐵− meson is 𝑏𝑢 ̅ quark combination.
a. Show that this is consistent for all quantum numbers
b. What are the quark combinations for 𝐵+, 𝐵0, �̅�0?
3. What are the quark combination that can form:
a. A neutron
b. An antineutron
c. A Λ0
d. A Σ̅0
238
9.6 COLOR IN FORMING OF BOUND STATES OF QUARKS.
Activity 9.6: Investigating the bound state of an atom.
Take the case of an electronic configuration of hydrogen atom. Make the illustration and then
contrast the interaction between electron and proton and bound state of elementary particles
9.6.1 Bound state of quarks
In the hydrogen atom configuration, the proton is located at centre while electron moves around it at
a speed of about 1% the speed of light. The proton is heavy while the electron is light (See Fig.9.3)
Fig.9. 3 The structure of Hydrogen atom (Strassler, 2011)
This is the simplest example of what physicists call a “bound state”. The word “state” basically just
meaning a thing that hangs around for a while, and the word “bound” meaning that it has
components that are bound to each other, as spouses are bound in marriage.
The inside of the proton itself is more like a commune packed full of single adults and children: pure
chaos. It too is a bound state, but what it binds is not something as simple as a proton and an
electron, as in hydrogen, or even a few dozen electrons to an atomic nucleus, as in more complicated
atoms such as gold, but zillions (meaning “too many and too changeable to count usefully”) of
lightweight particles called quarks, antiquarks and gluons. It is impossible to describe the proton’s
structure simply, or draw simple pictures, because it’s highly disorganized. All the quarks and
antiquarks and gluons (see Fig.9.4) inside are rushing around as fast as possible, at nearly the speed
of light (Strassler, 2011).
Fig.9. 4 Snapshot of a proton: Imagine all of the quarks (up, down, and strange: u, d, s), antiquarks (u, d, s with a
bar on top), and gluons (g) zipping around near the speed of light, banging into each other, and appearing and
disappearing (Strassler, 2011)
239
You may have heard that a proton is made from three quarks but this is not true. In fact there are
billions of gluons, antiquarks, and quarks in a proton.
9.6.2 Color in forming of bound states of quarks.
In the standard model of Quantum Chromodynamics (QCD) and the electroweak theory (Giancoli D.
C., Physics: principals with application, 2005), not long after the quark theory was proposed, it was
suggested that quarks have another property (or quality) called color, or ‘color charge’ (analogous
to electric charge). The distinction between the six quarks (u, d, s, c, b, t) was referred to as flavors.
According to the theory, each of the flavors of quark can have three colors, usually designated red,
green and blue. These are the three primary colors which, when added together in equal amounts, as
on a TV screen, produce white. Note that the names ‘color’ and ‘flavor’ have nothing to do with our
sense, but are purely whimsical as are other names, such as charm, in this new field. The antiquarks
are colored antired, antigreen and antiblue. Baryons are made up of three quarks, one of each color.
Mesons consist of quark-antiquark pair of a particular color and its anticolor. Both baryons and
mesons are thus colorless or white.
Originally, the idea of quark color was proposed to preserve the Pauli exclusion principle. Not all
particles obey the exclusion principle. Those that do, such as electrons, protons and neutrons, are
called fermions. Those that don’t are called bosons. These two categories are distinguished also in
their spin: bosons have integer spin (0, 1, etc) whereas fermions have half-integer spin, usualy 1
2 as
for electrons and nucleons, but other fermions have spin 2
5,
2
3etc. Matter is made up mainly of
fermions, but the carriers of forces (𝛾, 𝑊, 𝑍 and gluons) are all bosons. Quarks are fernions they have
spin2
1 and therefore should obey the exclusion principle. Yet for three particular baryons (uuu, ddd,
and sss), all three quarks would have the same quantum numbers, and at least two quarks have their
spin in the same quantum numbers, and at least two quarks have their spin in the same direction
(since there are only two choices, spin up (2
1sm ) or spin down (
2
1sm ). This would seem to
violate the exclusion principle; but if quarks have an additional quantum number (color), which is
different for each quark, it would serve to distinguish them and allow the exclusion principle to hold.
Although quark color, and the resulting threefold increase in the number of quarks, was originally an
adhoc idea, it also served to bring the theory into better agreement with experiment, such as
predicting the correct lifetime of the 𝜋0 meson. The idea of color soon became a central feature of
the theory as determining the force binding quarks together in hadron.
9.6.3 Colour as component of quarks and gluons
Activity 9.7: Investigating the origin of color
When a metal like iron is heated red-hot, one can observe the change in color. As the energy
increases, as the color changes. Use the same experiment and discuss on the following questions
1. As the color changes in the metal, what are the scientific reasons behind that?
2. Explain the matter − energy interaction and their consequences
3. What is color in the field of elementary particles?
240
The attractive interactions among quarks are mediated by massless spin −1 bosons called gluons in
much the same way that photons mediate the electromagnetic interaction or that pions mediated the
nucleon–nucleon force in the old Yukawa theory (Nagashima, 2013).
Particles were classified into two categories:
Quarks and leptons have an intrinsic angular momentum called spin, equal to a half-integer (1
2) of the
basic unit and are labeled as fermions. Fermions obey the exclusion principle on which the Fermi-
Dirac distribution function is based. This would seem to forbid a baryon having two or three quarks
with the same flavor and same spin component. To avoid this difficulty, it is assumed that each quark
comes in three varieties, which are called color: red, green, and blue. The exclusion principle applies
separately to each color. Particles that have zero or integer spin are called bosons. Bosons do not
obey the exclusion principle and have a different distribution function, the Bose-Einstein
distribution.
A baryon always contains one red, one green, and one blue quark, so the baryon itself has no net
color.
Each gluon has a color–anticolor combination (for example, blue–antired) that allows it to
transmit color when exchanged, and color is conserved during emission and absorption of a gluon
by a quark.
The gluon-exchange process changes the colors of the quarks in such a way that there is always
one quark of each color in every baryon. The color of an individual quark changes continually as
gluons are exchanged.
Similar processes occur in mesons such as pions:
The quark–antiquark pairs of mesons have canceling color and anticolor (for example, blue and
antiblue), so mesons also have no net color. Suppose a pion initially consists of a blue quark and
an antiblue antiquark.
The blue quark can become a red quark by emitting a blue–antired virtual gluon.
The gluon is then absorbed by the antiblue antiquark, converting it to an antired antiquark (Fig. 9.8).
Color is conserved in each emission and absorption, but a blue–antiblue pair has become a red–
antired pair. Such changes occur continually, so we have to think of a pion as a superposition of three
quantum states:
blue–antiblue,
green–antigreen, and
red–antired.
In terms of quarks and gluons, these mediating virtual mesons are quark–antiquark systems bound
together by the exchange of gluons.
241
Fig.9. 5 (a) A pion containing a blue quark and an antiblue antiquark. (b) The blue quark emits a blue–antired
gluon, changing to a red quark. (c) The gluon is absorbed by the antiblue antiquark, which becomes an antired
antiquark. The pion now consists of a red–antired quark–antiquark pair. The actual quantum state of the pion is
an equal superposition of red–antired, green antigreen, and blue–antiblue pairs.
9.6.4 Checking my understanding
1. Label the illustration below and analyze the interaction between its particles.
Fig.9. 6 Illustration diagram
1. Define and describe the following key concept:
i. Color charge:
ii. Gluons
iii. Quantum chromodynamics
5. Which one of the following sets of color combinations is added in color vision in TV’?
A. Red, green and blue C. White. red and yellow
B. Orange, back and violet D. Yellow, green and blue
6. What are the color composition of
a. Gluons
b. Meson
c. Baryon
9.7 END UNIT ASSEMENT
9.7.1 Multiple choices
1. A proton is made up of
242
A. one up quark and two down quarks C. two up quarks and a down quark
B. an up quark and down antiquark D. strange quark and an anti-strange quark
2. Particles that are unaffected by strong nuclear force are
A. protons C. neutrons
B. leptons D. bosons
3. Particle which explains about mass of matter is called
A. Higgs boson C. protons
B. Leptons D. neutrons
4. A conservation law that is not universal but applies only to certain kinds of interactions is
conservation of:
A. lepton number D. charge
B. baryon number E. strangeness
C. spin
5. In quantum electrodynamics (QED), electromagnetic forces are mediated by
A. the interaction of electrons. D. the weak nuclear interaction.
B. hadrons. E. the exchange of virtual photons.
C. action at a distance.
6. Conservation laws that describe events involving the elementary particles include the conservation
of
A. energy. D. electric charge.
B. All of these are correct. E. baryon and lepton numbers.
C. linear and angular momentum.
7. The conservation law violated by the reaction ep 0 is the conservation of
A. charge. D. lepton number and baryon number.
B. energy. E. angular momentum.
C. linear momentum.
8. Particles that participate in the strong nuclear interaction are called
A. neutrinos D. electrons
B. hadrons E. photons
C. leptons
9.7.2 Structured questions
9. In the table cross-word below, find at least fifteen names associated to elementary particles.
Among them, select ones that represents quarks, leptons or radiations.
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M K L G T B A V A E K X R A Y
E N A T H A N A S L J Y A M V
S Q U A R K Z L N E U C L E I
O A M U R C B E G C L P P N L
N P N E M I L L E T L H H K U
K S E V A R I S T R E Y O A N
X I M B E T A K A O N S N B G
R C A G L A S P I N Z I S A A
A O K A L P H A L E I C I R O
P L A M D A T I V U O S N Y S
R O Q M K A N E U T R I N O B
O R T A G M I N O R W A N N E
T U S G A U G E B O S O N G R
O L E P T O N B E N O N C A T
N I Y D O N A T P A T R I C K
10. (A) Making massive particles: Relatively massive particles like the proton and neutron are made
of combinations of three quarks.
i. What is the charge on the combination uuu?
ii. What is the charge on the combination uud?
iii. What is the charge on the combination udd?
iv. What is the charge on the combination ddd?
(B) There are four compound particles here
i. Which combination has the right charge to be a proton?
ii. Which combination has the right charge to be a neutron?
iii. There is a particle called the which has a charge of –1e. Which quark combination could be
the ?
iv. There is a particle called the which has a charge of + 2e. Which quark combination
could be the ∆−?
v. A neutron can be changed to a proton if one quark changes ‘flavour’. What change is needed?
What charge must be carried away if this happens?
(C) Making mesons
Other, lighter ‘middle-weight’ particles called mesons can be made from pairs of quarks. But they
have to be made from a special combination: a quark and an antiquark. There are now four particles
to play with: Up quark u: charge +2/3 e, Down quark d: charge –1/3 e, Antiup quark u : charge –2/3
e. Antidown quark d : charge + 1/3 e.
11.
(i) What is the charge on the combination u u ?
(ii) What is the charge on the combination d d ?
(iii) What is the charge on the combination u d ?
244
(iv) What is the charge on the combination d u ?
(v) Which combination could be the 𝜋+ meson?
(vi) Which combination could be the 𝜋−meson?
(vii) Which could be the neutral 𝜋0meson?
12. Identify the missing particle in the following reactions.
(a) p + p → p + n + π++?
(b) p+? → n + μ+
13. Which of the following reactions are possible, and by what interaction could they occur? For
those forbidden. Explain why.
(a) 𝜋− + 𝑝 → 𝐾+ + 𝛴−
(b) 𝜋+ + 𝑝 → 𝐾− + 𝛴−
(c) 𝜋− + 𝑝 → 𝛬0 + 𝐾0 + 𝜋0
(d) 𝜋+ + 𝑝 → 𝛴0 + 𝜋0
(e) 𝜋− + 𝑝 → 𝑝 + 𝑒− + �̅�𝑒
14. Determine which of the following reactions can occur. For those that cannot occur, determine the
conservation law (or laws) violated.
(a) p → π+ + π0
(b) p + p → p + p + π0
(c) p + p → p + π+
(d) π+ → μ+ + νμ
(e) n → p + e− + ν̅e
(f) π+ → μ+ + n
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UNIT10: EFFECT OF X-RAYS
X rays are today most used at hospitals in radiology service for imaging purpose.
Key unit Competence
By the end of the unit, I should be able to analyze and evaluate the effects of X-rays.
My goals
− Explain the production of X-rays
− State the properties of X-rays.
− Explain the origin and characteristic features of an x-ray spectrum.
− Outline the applications of X-rays in medicine, industries, and scientific research
− Solve problems involving accelerating potential and minimum wavelength of X-rays.
− Recognize how the intensity and quality of X-rays can be controlled.
− Appreciate the use of X-rays in medicine and industry
INTRODUCTORY ACTIVITY
When a person goes to the hospital with pain in her/his chest, or with an internal fracture of the bone,
physicians do normally recommend the patient to pass by radiology service. Hence try to answer the
following questions:
1. Why do physicians recommend patients to pass by radiology service?
2. Radiology means that there are radiations. Discuss different types of radiations that are found in
there?
3. Discuss the production of X-ray radiations.
4. What are the positive and negative effects of X-ray radiation on the human body?
246
10.1 PRODUCTION OF X-RAYS AND THEIR PROPERTIES
Activity 10.1: Investigating the production of X-rays
Read the following text and answer the questions that follow.
Discovery of X-rays: Becquerel’s discovery wasn’t the only important accidental one. In the
previous year W.C. Roentgen unexpectedly discovered X-rays while studying the behavior of
electrons in a high-voltage vacuum tube. In that instance, a nearby material was made to fluoresce.
Roentgen named them X- rays because he didn’t know what they were. Within twenty years of this
discovery, diffraction patterns produced using X-rays on crystal structures had begun to show the
finer structure of crystals while, at the same time, giving evidence that X-rays had a wave nature.
Since then, X-ray radiation has become an indispensable imaging tool in medical science.
Questions:
1. What do you understand by X-rays?
2. How are X-rays produced?
3. Where are X-rays used?
10.1.1 X-ray production
X-rays are produced when fast moving electrons strike matter (see Fig.10.1). They were first
produced in 1895 by Wilhelm Rontgen (1845-1923), using an apparatus similar in principle to the
setup shown in Fig.10.1. Electrons are emitted from the heated cathode by thermionic emission and
are accelerated toward the anode (the target) by a large potential difference V. The bulb is evacuated
(residual pressure atm710 or less), so that the electrons can travel from the cathode to the anode
without colliding with air molecules. It was observed that when V is a few thousands volts or more, a
very penetrating radiation is emitted from the anode surface.
Fig.10.1: The Coolidge tube, also called hot cathode tube or X-ray tube.
The above figure is an illustration of the Coolidge tube which is the most widely used device for the
production of X-rays. The electrons are produced by thermionic effect from filament, which is the
cathode of the tube, heated by an electric current. These electrons are accelerated towards a metal
247
target that is the anode due to the high potential voltage between the cathode and the anode. The
target metals are normally Tungsten or Molybdenum and are chosen because they have high melting
point and higher atomic weights. The accelerated electrons interact with both electrons and nuclei of
atoms in the target and a mysterious radiation is emitted. This radiation was referred to as X-rays.
About 98% of the energy of the incident electron is converted into heat that is evacuated by the
cooling system and the remaining 2% come out as X-rays.
10.1.2 Types of X-rays
Sometimes X-rays are classified according to their penetrating power. Two types are mentioned:
- Hard X-rays: those are X-rays on upper range of frequencies or shorter wavelength. They
have greater energy and so they are more penetrating.
- Soft X-rays: they are X-rays on lower range of frequencies or longer wavelength. They have
lower energy and they have very low penetrating power. The Fig.10.2 below shows the relative
location of the different types of X-rays.
Hard X-rays are produced by high accelerating potential. They have high penetrating power and
short wavelength while soft X-rays are produced by lower accelerating potential, have relatively low
penetrating power and relatively long wavelength
Fig.10. 2: The location of x-ray in the electromagnetic spectrum.
10.1.3 Properties of X-rays
Activity 10.2: Understanding the pros and cons of X-rays
Make intensive research on the production and the properties of X-rays, then write a report about
your findings.
The following are the main properties of X-rays:
(a) X-rays can penetrate through most substances. However, their penetrating power is different.
(b) X-ray can produce fluorescence in different substances.
248
(c) X-rays can blacken photographic plate. The degree of blackening depends upon the intensity of
x-rays incident upon the plate. Thus, X-ray intensity can be measured with the help of
photographic plates.
(d) X-rays ionize the gas through which they travel. The ionizing power depends on the intensity
of the x-ray beam. Thus, X-ray intensity can also be measured by measuring their ionizing
power.
(e) X-rays are not deflected by electric or magnetic fields. This proves that unlike cathode rays or
positive rays they are not a beam of charged particles.
(f) X-rays travels on a straight lines like ordinary light.
(g) X-ray are both reflected and refracted.
(h) X-rays can be diffracted with the help of crystalline substances. They can also be polarized.
From the above characteristics it can be seen that X-rays have the properties that are common to all
electromagnetic radiations.
10.1.4 Checking my progress
1. Describe the process by which X-rays are produced.
2. Discuss and describe the types of X-rays?
3. What is the meaning of the X in X-ray?
4. How are X-rays different from other electromagnetic radiations?
5. What are the main properties of X-rays?
249
10.2 THE ORIGINS AND CHARACTERISTIC FEATURES OF AN X-RAY
SPECTRUM
Activity 10.3 investigating the X-ray spectrum
During the production of X-rays, a high voltage must be applied across the x rays tube to produce
enough acceleration of electrons towards the target.
Search internet, then discuss and explain the relationship between the applied voltage, the wave
length and the characteristics of the produced X-ray.
10.2.1 Variation of the X-ray intensity with wavelength
Depending on the accelerating voltage and the target element, we may find sharp peaks
superimposed on a continuous spectrum as indicated on Fig.10.3. These peaks are at different
wavelengths for different elements; they form what is called a characteristic x-ray spectrum for each
target element.
Fig.10.3: Intensity as a function of the wavelength of x-rays emitted at a particular voltage.
X-rays of different wavelengths are emitted from X-ray tube. If the intensity is measured as a
function of the wavelength and the variation is plotted graphically then a graph of the nature shown
on the figure above is obtained. The graph has the following features,
(a) Minimum wavelength
(b) Continuous spectrum
(c) Characteristic peaks
250
10.2.2 Origin of the continuous spectrum
It is known that when charged particles such as electrons are accelerated or decelerated they emit
electromagnetic radiation of different frequencies. In doing so a part of their kinetic energy is
transformed in the energy of the emitted radiation. Electrons inside the x-ray tube decelerate upon
hitting the target and as a result they emit electromagnetic radiations with a continuous distribution
of wavelength starting from a certain minimum wavelength. This mechanism of producing
electromagnetic radiation from an accelerated or decelerated electron is called bremsstrahlung.
The energy of the emitted photon is given by
hchfE , (10.01)
where sJh 34106260.6 is the Planck constant and 𝑐 = 3.0𝑥108 𝑚/𝑠 the speed of light in
vacuum.
The maximum energy of the emitted photons is therefore equal to the energy of the incident electron:
min
hceVE (10.02)
Where 𝜆𝑚𝑖𝑛is the minimum wavelength, V is the potential difference between anode and cathode
and e the charge of the electron.
If V is measured in volts we get
0
min
12413A
V (10.03)
Thus if 𝑉 = 1000 𝑣𝑜𝑙𝑡𝑠 then oA24.1min and if 𝑉 = 5000 𝑣𝑜𝑙𝑡𝑠 then oA248.0min
As the many electrons in the X-ray are decelerated differently, this will result in a continuous
spectrum of the emitted wavelengths.
251
Fig.10.4: Intensity as a function of the wavelength of x-rays emitted at a particular voltage.
It can be observed from the above Fig.10.4 that, for different values of the accelerating voltage, the
minimum wavelength decreases with increasing potential difference and for a given wavelength the
intensity is higher when the potential difference is higher.
10.2.3 Origin of characteristic lines
The peaks observed in wavelengths distribution curves as shown in Fig. 10.4 are spectral lines in the
X-ray region. Their origin lies in the transition between energy levels in the atoms of the target.
The electrons in the atoms are arranged in different atomic shell. Of these, the first two electrons
occupy the K-shell followed by 8 electrons in the L-shell, 18 electrons in the M-shell and so on until
the electron in the target are used up. A highly accelerated electron may penetrate atom in the target
and collide with an electron in K-shell. If such electron is knocked out it will leave an empty space
that is immediately filled up by another electron probably from the L-shell or M-shell. This transition
will be accompanied by the emission of the excess energy as a photon.
The energy of the emitted photon is a characteristic of the energy levels in the particular atom and is
given by
LK
KL
KL EEhc
hf
(10.04)
For a transition between K and L-shells.
Thus the energy of the emitted photon depends on the binding energies in the K and L shells and
hence the x-ray spectral lines have definite frequencies and wavelengths which are characteristic of
the target atom.
For a given target material more than one spectral lines are observed as transitions may occur
between different energy levels.
252
Fig.10.5: X-ray emission line due to transition of electron between levels.
The X-ray lines originating from the transition between the different electron levels are usually
labelled by the symbols α, β, γ, etc.
From L-level to K-level transition produces Kα-line
From M-level to K-level transition produces Kβ –line
From M-level to L-level transition produces Lα –line
From N-level to L- level transition produces Lβ –line
10.2.4 Checking my progress
1. What is the characteristic of X-ray characteristic peak radiation?
2. How is X-ray continuum produced via bremsstrahlung?
3. X-rays are generated when a highly accelerated charged particle such as electrons collide with
target material of an X-ray tube. The resulting X-rays have two characteristics: the continuous X-rays
(also called white X-rays) and characteristic X-rays peaks. The wavelength distribution and intensity
of continuous X-rays are usually depending upon the applied voltage and a clear limit is recognized
on the short wavelength side.
a. Estimate the speed of electron before collision when applied voltage is 30kV and compare it with
the speed of light in vacuum.
b. In addition, establish the expression of the shortest wavelength limit 𝜆𝑚𝑖𝑛 of X-rays generated
with the applied voltage V. it is obtained when the incident electron loses all its energy in a single
collision.
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10.3 APPLICATIONS AND DANGERS OF X-RAYS
Activity 10.4: Investigation of X-rays uses and dangers
1. Using the historical background of X-ray discovery, what are the uses of X-rays in real life?
2. Discuss the dangers that X-rays may cause when they are used in a wrong way.
X-rays have many practical applications in medicine and industry. Because X-ray photons are of
such high energy, they can penetrate several centimetres of solid matter. Hence they can be used to
visualize the interiors of materials that are opaque to ordinary light, such as broken bones or defects
in structural steel.
10.3.1 In medicine
Fig.10.7: The radiology of human body using x-rays
X-ray imaging utilizes the ability of high frequency electromagnetic waves to pass through soft parts
of the human body largely unimpeded. For medical applications, parts of the human body are
exposed to moderated X-rays intensity and images are produced in similar way as light on a
photographic plate or digital recorder to produce a radiograph (See Fig.10.7). By rotating both source
and detector around the patient’s body a “slice” image can be produced in what is called
computerized tomography (CT). Although CT scans expose the patient to higher doses of ionizing
radiation the slice images produced make it possible to see the structures of the body in three
dimensions.
In 1895, the Dutch Wilhelm Roentgen (See Fig.10.8) discovered that light energy could be used to
take photographs through substances such as paper, cloths and wood. Roentgen also discovered that
this invisible form of light energy, called X-rays could be used to take the pictures of structures
inside the body as shown in Fig. below. Bone tissue appears clearly on an X-rays.
254
The object to be visualized is placed between an X-ray source and an electronic detector (like that
used in a digital camera) or a piece of photographic film (Fig.10.8 or Fig.10.8B). The darker area in
the recorded images by such a detector, the greater the radiation exposure. Bones are much more
effective X-ray absorbers than soft tissue, so bones appear as light areas. A crack or air bubble allows
greater transmission and shows as a dark area.
Fig.10.8: An X-ray picture (B) (radiograph) taken by Rontgen (A) of Albert von Kölliker's hand.
A widely used and vastly improved x-ray technique is computed tomography; the corresponding
instrument is called a CT scanner. The x-ray source produces a thin, fan-shaped beam that is detected
on the opposite side of the subject by an array of several hundred detectors in a line. Each detector
measures absorption along a thin line through the subject. The entire apparatus is rotated around the
subject in the plane of the beam, and the changing photon-counting rates of the detectors are
recorded digitally. A computer processes this information and reconstructs a picture of absorption
over an entire cross section of the subject
In the middle 1970, CT (Computer Tomography) scanning machines were introduced in human
medicine.
X-rays are also used in the following:
- Killing of cancerous cells
- Radiography is also used in industry for examining potentially damaged machinery to ascertain
the cause of damage and to verify castings or welded joints
- X-rays are used to study the structure of crystals (crystallography).
- When a handgun is fired, a cloud of gunshot residue (GSR) is ejected from the barrel. The x-ray
emission spectrum of GSR includes characteristic peaks from lead (Pb), antimony (Sb), and
barium (Ba). If a sample taken from a suspect’s skin or clothing has an x-ray emission spectrum
with these characteristics, it indicates that the suspect recently fired a gun.
255
10.3.2 Examining luggage cargo and security.
Fig.10. 9: Trailer carrying a car on check by X-rays
X-rays are being used in airports to examine luggage for weapons or bombs. Note that the metal
detector that you walk through in the airport does not X-ray you. It uses magnetic waves to detect
metal objects. X-rays are also being used to examine cargo luggage for illegal or dangerous material
as in Fig.10.9.
10.3.3 In industry
Fig.10.10: The view of cracks in metals checked by using X-rays
They can be used to detect structural problems and cracks in metals that cannot be seen from the
outside. X-rays are used on commercial airplanes, bridges metals and pipe lines, to make sure there
are no stress fractures or other dangerous cracks in the material.
256
10.3.4 In scientific research
X-ray diffraction provides one of the most important tools for examining the three-dimensional
(3D) structure of biological macromolecules and cells.
They are also used in crystallography, where X-ray diffraction and scattered waves show the
arrangement of atoms in the crystal.
Fig.10.31: Schematic diagram of the technique used to observe the crystal structure by x-rays diffraction.
The array of spots formed on the film is called a Laue pattern and show the atom structure of the
crystal.
10.3.5 Dangers of X-rays
X rays cause damage to living tissues. As X-ray photons are absorbed in tissues, their energy
breaks molecular bonds and creates highly reactive free radicals (such as neutral H and OH),
which in turn can disturb the molecular structure of proteins and especially genetic material.
Young and rapidly growing cells are particularly susceptible, which is why X-rays are useful for
selective destruction of cancer cells.
Because X-rays can kill living cells, they must be used with extreme care. When improperly used
they can cause severe burns, cancer, leukemia, and cataracts. They can speed aging, reduce
immunity to disease, and bring about disastrous changes in the reproductive cells.
Lead screens, sheets of lead-impregnated rubber, and leaded glass are used to shield patients and
technicians from undesired radiation.
The effect of X-ray radiations is cumulative. That is, many minor doses over a number of years is
equivalent to a large dose at one time.
Unnecessary exposure to x-rays should be avoided. MRI (Magnetic Resonance Imaging) uses
magnets and sound energy to form pictures of the internal organs without exposing patients to
harmful X-rays.
When they are used in hospitals, the sources should be enclosed in lead shields.
A careful assessment of the balance between risks and benefits of radiation exposure is essential in
each individual case.
10.3.6 Safety precaution measures of dangers caused by X-rays
Medical and dental X-rays are of very low intensity, so that the hazard is minimized. However, X-ray
technicians who go frequently behind the lead shield while operating X-rays need to be protected
because of the frequency of exposure. A person can receive many medical or dental X-rays in a year
257
with very little risk of getting cancer from it. In fact, exposure to natural radiation such as cosmic
rays from space poses a greater risk.
The following are some of the precautions:
(i) Protective suits and wears such as gloves and eye glasses made of lead are used always when
handling these radiations. These shields protect the workers from X-ray exposure.
(ii) Workers who operate equipment’s that use X-rays must wear special badges which detect the
amount of radiation they are exposed to.
(iii) Food and drinks are not allowed in places where X-radiations are present.
(iv) Experiments that involve these radiations (X-rays) substances should be conducted in a room
surrounded by thick concrete walls or lead shields.
(v) Equipment that use X-rays should be handled using remote-controlled mechanical arms from a
safe distance.
10.3.7 Checking my progress
1. How do we create different X-ray images in medicine?
2. What are the dangers that may be caused by using excessive dose of X-rays?
258
10.4 PROBLEMS INVOLVING ACCELERATING POTENTIAL AND MINIMUM
WAVELENGTH.
10.4.1 Accelerating potential and minimum wavelength
Activity 10.5 Calculation of accelerating potential in X-ray tube
An x-rays tube operates at 30 kV and the current through it is 2.0 mA. Calculate:
a. The electrical power output
b. The number of electrons striking the target per second.
c. The speed of the electrons when they hit the target
d. The lower wavelength limit of the X-rays emitted.
When a high voltage with several tens of kV is applied between two electrodes, the high-speed
electrons with sufficient kinetic energy is drawn out from the cathode and collides with the anode. The
electrons rapidly slow down and lose kinetic energy.
Since the slowing down patterns (method of losing kinetic energy) varies with electrons, continuous
X-rays with various wavelength are generated. When an electron loses all its energy in a single
collision, the generated X-ray has the maximum energy (or the shortest wavelength λSWL ). The
value of the shortest wavelength limit can be estimated from the accelerating voltage V between
electrodes.
maxhfeV (10.07)
𝜆𝑆𝑊𝐿 =𝑐
𝑓𝑚𝑎𝑥=
ℎ𝑐
𝑒𝑉 (10.08)
Because X-rays are emitted by accelerated charges, x-rays are electromagnetic waves. Like light, X-
rays are governed by quantum relationships in their interaction with matter. Thus, we can talk about
X-ray photons or quanta, and the energy of an X-ray photon is related to its frequency and
wavelength in the same way as for photons of light,
hchfE (10.09)
Typical X-ray wavelengths are m1210 to m910 . X-ray wavelength can be measured quite
precisely by crystal diffraction techniques. X-ray emission is the inverse of the photoelectric effect.
In photoelectric emission there is a transformation of the energy of a photon into the kinetic energy
of an electron, in X-ray production there is a transformation of the kinetic energy of an electron into
energy of a photon.
In X-ray production we usually neglect the work function of the target and the initial kinetic energy
of the boiled off electrons because they are very small in comparison to the other energies.
259
Example 10.1
1. Electrons in an X-ray tube accelerate through a potential difference of 10.0 kV before striking a
target. If an electron produces one photon on impact with the target, what is the minimum
wavelength of the resulting X- rays? (Answer using both SI units and electron volts.
Answer
To produce an x-ray photon with minimum wavelength and hence maximum energy, all of the
electron’s kinetic energy must go into producing a single x-ray photon. We’ll use Eq. (10.09) to
determine the wavelength
𝜆𝑚𝑖𝑛=
ℎ𝑐
𝑒𝑉=
(6.63𝑥10−34 𝐽.𝑠)(3𝑥108 𝑚/𝑠)
(1.6𝑥10−19𝐶)(10.0𝑋103 𝑣𝑜𝑙𝑡𝑠)=1.24𝑥10−10𝑚=0.124 𝑛𝑚
Using electron volts, we have
nmVe
smseV
eV
hchf
AC
124.0)100.10(
)/103)(10136.4(3
815
maxmin
Bragg's Law
According to W. L. Bragg ( (Weseda, Mastubara, & Shinoda, 2011), X-ray diffraction can be viewed
as a process that is similar to reflection from planes of atoms in the crystal. In Bragg's construct, the
planes in the crystal are exposed to a radiation source at a glancing angle θ and X rays are scattered
with an angle of reflection also equal to θ. The incident and diffracted rays are in the same plane as
the normal to the crystal planes (Fig.10. 4).
Fig.10. 4 Bragg’s construction of x rays diffraction by a crystal
260
Constructive interference occurs only when the path difference between rays scattered from parallel
crystal planes would be an integer number of wavelengths of the radiation. When the crystal planes
are separated by a distance d, the path length difference would be 2dsin θ.
Thus, for constructive interference to occur the following relation must hold true.
𝑛𝜆 = 2𝑑𝑠𝑖𝑛𝜃 (10.10)
This relation is known as Bragg's Law.
Thus for a given d spacing and wavelength, the first order peak (n = 1) will occur at a particular θ
value. Similarly, the θ values for the second (n = 2) and higher order (n > 2) peaks can be
predicted.
From eVmv 2
2
1 and mvp where
hp
m
eVv
2 and mvp so
mv
h
Then eVm
nh
m
eVm
nhd
22sin2
where
emeV
h
2 is he de Broglie wavelength
De Broglie relation can also be written as 027.12A
V where mA 100 10
The above derivation assumes that phase differences between wavelengths scattered at different
points depend only on path differences. It is assumed that there is no intrinsic phase change between
the incident and scattered beams or that this phase change is constant for all scattering events.
Example 10.2
1. Monochromatic X-rays of wavelength 1.2 × 10−10 m are incident on a crystal. The 1storder
diffraction maximum is observed at when the angle between the incident beam and the atomic
plane is 120.What is the separation of the atomic planes responsible for the diffraction?
Answer:
According to Bragg’s law sin2dn and n = 1
Therefore 𝜆 = 2𝑑 sin 𝜃 ⇔ 𝑑 =𝜆
2 sin 𝜃=
(1.2𝑥10−10)𝑚
2 sin 12= 2.89𝑥10−10𝑚
261
10.4.2 Checking my progress
1. Calculate
a. strength of the electric field E,
b. force on the electron F,
c. acceleration a of electron, when a voltage of 10 kV is applied between two electrodes separated
by an interval of 10 mm.
2. Crystal diffraction experiment can be performed using X-rays, or electrons accelerated through
appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the
wavelength of the probe equal to1Å, which is of the order of inter- atomic spacing in the lattice)
(me = 9.11×10−31kg).
262
10.5 END UNIT ASSESSMENT
10.5.1 Multiple choices
1. Choose the letter that best matches the true answer:
(i) X-rays have
A. short wavelength C. both A and B
B. high frequency D. longest wavelength
(ii) If fast moving electrons rapidly decelerate, then rays produced are
A. alpha rays C. beta rays
B. x-rays D. gamma rays
(iii) Energy passing through unit area is
A. intensity of x-ray C. wavelength of x-ray
B. frequency of x-ray D. amplitude of x-ray
(iv) X-rays are filtered out of human body by using
A. cadmium absorbers C. copper absorbers
B. carbon absorbers D. aluminum absorbers
(v) Wavelength of x-rays is in range
A. 10-8 m to 10-13 m C. 10-10 m to 10-15 m
B. 10-7 m to 10-14 m D. 10² m to 109 m
10.5.2 Structured questions
2. A plot of x-ray intensity as a function of wavelength for a particular accelerating voltage and a
particular target is shown in Fig.10.5.
263
Fig.10. 5Characteristics of x rays spectrum
a. There are two main components of this x-ray spectrum: a broad range of x-ray energies and a
couple of sharp peaks. Explain how each of these arises.
b. What is the origin of the cut-off wavelength min of the Fig.10.5 shown below? Why is it an
important clue to the photon nature of x-rays?
c. What would happen to the cut-off wavelength if the accelerating voltage was increased? What
would happen to the characteristic peaks? Use a sketch to show how this spectrum would look if
the accelerating voltage was increased.
d. What would happen to the cut-off wavelength if the target was changed, keep the same
accelerating voltage? What would happen to the characteristic peaks? Use a sketch to show how
the spectrum would look if some other target material was used, but the accelerating voltage was
kept the same.
3. Electrons are accelerated from rest through a p.d of 10 kV in an x ray tube. Calculate:
i. The resultant energy of the electrons in eV.
ii. The wavelength of the associated electron waves. (1.23x10-11m)
ii. The maximum energy and the minimum wavelength of the x ray radiation generated (assume, me,
e, sJh 341062.6 , smc /103 8 : (1.6 × 10−15 J, 1.24 × 10−10m)
4. Monochromatic X-ray of wavelength 1.2 × 10−10 𝑚 are incident on a crystal. The 1storder
diffraction maximum is observed at when the angle between the incident beam and the atomic plane
is120.What is the separation of the atomic planes responsible for the diffraction?
5. An x-ray operates at 30 kV and the current through it is 2.0 mA. Calculate:
(i) The electrical power output
(ii) The number of electrons striking the target per second.
(iii) The speed of the electrons when they hit the target
(iv) The lower wavelength limit of the x-rays emitted.
6. An x-ray machine can accelerate electrons of energies4.8 × 10−15J. The shortest wavelength of
the x- rays produced by the machine is found to be 4.1 × 10−11m. Use this information to estimate
the value of the plank constant.
264
7. The spacing between Principal planes of NaClcrystal is 2.82 Å . It is found that the first order
Bragg diffraction occurs at an angle of 100. What is the wavelength of the x rays?
8. What is the kinetic energy of an electron with a de Broglie wavelength of 0.1 nm. Through what
p.d should it be accelerated to achieve this value? Assume e, me, h.
9. You have decided to build your own x-ray machine out of an old television set. The electrons in
the TV set are accelerated through a potential difference of 20 kV. What will be the min for this
accelerating potential?
10. A tungsten target (Z = 74) is bombarded by electrons in an x-ray tube. The K, L, and M atomic x-
ray energy levels for tungsten are -69.5, -11.3 and -2.30 keV, respectively.
a. Why are the energy levels given as negative values?
b. What is the minimum kinetic energy of the bombarding electrons that will permit the production
of the characteristic K and K lines of tungsten?
c. What is the minimum value of the accelerating potential that will give electrons this minimum
kinetic energy?
d. What are the K and K wavelengths?
11. Using the following illustration figure Fig.10.6, label each part marked by letter from A to H and
explain the function of each part A, B, C, D, E, F and H.
Fig.10. 6 X ray tube illustration
265
UNIT 11: EFFECTS OF LASER.
Key unit Competence
By the end of this unit I should be able to analyze the application of LASER.
My goals
- Define a laser beam
- Explain the stimulated emission of light
- Explain the spontaneous emission of light
- Analyse the mechanism to produce LASER beam - Explain laser properties
- Explain and describe monochromatic and coherent sources of light
- Analyse a LASER light as a source of coherent light. - Explain the principle and uses of Laser.
- Outline applications of LASER
- Analyse applications and dangers of LASER beam
- Analyse precautional measures of the negative effects of Laser.
INTRODUCTORY ACTIVITY
A man has tied all forms of advancements from traditional methods of solving problems to advanced
methods by use of different technologies. Among other technological advancements, discovery of
Laser that is a part of visible light under electromagnetic waves has had a great impact in solving
many of our problems.
a) What do you understand by Electromagnetic waves?
b) Discuss at least four (4) characteristics of Electromagnetic waves
c) In your own words, discuss how these electromagnetic waves are produced.
266
d) Are all kinds of these electromagnetic waves have the same energy? If Yes why? If No, why not?
e) Basing on what you know about these electromagnetic waves, what could be positive uses of
these waves. Also discuss negative effects of electromagnetic waves.
f) How are electromagnetic waves related to LASERS?
11.1 Concept of LASER
Activity 11.1
a) From your own understanding, explain how a LASER light is produced.
b) Does production, need source of energy like electricity. Explain your reasoning.
c) In energy levels, particles are either in ground or excited states. Is laser formed when particles or
electrons are in ground or excited states? Explain your reasoning.
The acronym LASER stands for Light Amplifier by Stimulated Emission of Radiation. This
expression means that the light is formed by stimulating a material's electrons to give out the laser
light or radiation.
The laser is a device that uses the ability of some substances to absorb electromagnetic energy and
re-radiate it, as a highly focused beam of monochromatic and synchronized wavelength radiation. In
1953 Charles H. Townes, with graduate students James P. and Herbert J., produced the first
Microwave Amplifier by Stimulated Emission of Radiation (MASER), as a device operating in the
same way as a laser, but amplifying microwave radiations. This system could release stimulated
emissions without falling to the ground state, and thus maintaining a population inversion. A laser is
a device that emits light through a process of optical amplification based on the stimulated emission
of electromagnetic radiation. That is, the laser is a light source that produces a beam of highly
coherent and very nearly monochromatic light because of cooperative emission from many atoms.
11.1.1 Absorption, Spontaneous emission and Stimulated emission
Activity 11.2
1. Using scientific explanations, Explain the meaning of the following terms
i) Absorption
ii) Stimulated emission
iii) Spontaneous emission
2. Electrons can jump from excited to ground state; does it absorb or radiate energy. Explain your
reasoning.
3. Write an equation that would be used to calculate the energy radiated by an electron when it jumps
from one energy level to another. Explain each term used in the equation.
4. What do you understand by the term population inversion?
a) Absorption
267
During the process of absorption, a photon from the source is destroyed and the atom which was at
the ground state is promoted to the excited state.
Fig.11. 1 Absorption process
If on is the number of atoms per unit volume in the ground state with energy Eg, then the number of
atoms per unit volume in the excited state of energy Eex at temperature T, will depend on both the
thermal energy and the difference between the energy levels and is given by
KT
E
enn
0 ,
where KJk /1038.1 23 and E is the difference between energy levels, E=Eex-Eg
Let 1n and 2n be the number of atoms per unit volume in the states of energies 1E and 2E
respectively. The ratio between the population of the two levels is ,
kT
EE
en
n 12
1
2
If 12 EE then 𝑛2 < 𝑛1 (as the right side of the equation is less than a unit i.e. 𝐸2 − 𝐸1 ≫ 𝑘𝑇
In normal cases the excited states are less populated than the ground state.
b) Spontaneous emission.
An atom or an electron can move from one energy level to another. A photon is released when an
electron moves from a higher energy level to a lower energy level. The release of photon (a particle
of light) is called spontaneous emission
At the excited state, an atom will drop to a lower level by emitting a photon of radiation in a process
called spontaneous emission. It emits the photon spontaneously after an average time called the
spontaneous lifetime of the level. This time depends on the atomic species; some levels have long
lifetime measured in seconds, whereas others are relatively short on the order of nanoseconds or less.
This lifetime determines the ability of the emitting atom to store energy and will affect the efficiency
of sources.
268
Fig.11. 2 Process of spontaneous emission
When an excited atom, depending on its lifetime at the higher energy level, comes down to lower energy
level, a photon is emitted, corresponding to the equation,
where
- h is the Planks constant,
- f is the frequency of the emitted photon
- E2 and E1 correspond to higher and lower energy levels respectively.
This process of spontaneous emission is a random process and the probability of such transition depends on
the number of atoms in the excited state 𝑛2.The number of such transition per unit volume per second is A21𝑛2
where A21 is known as the Einstein’s constant.
c) Stimulated emission
Stimulated emission occurs when a photon strikes an atom that is excited state and makes the atom emit
another photon
In stimulated emission (Fig. 11.3), each incident photon encounters a previously excited atom. A kind of
resonance effect induces each atom to emit a second photon with the same frequency, direction, phase, and
polarization as the incident photon, which is not changed by the process. For each atom there is one photon
before a stimulated emission and two photons after—thus the name light amplification. Because the two
photons have the same phase, they emerge together as coherent radiation.
Fig.11. 3: Stimulated emission process
Let us now suppose that the atom is found initially in level 2 and that an electromagnetic wave of frequency
off (i.e. equal to that of the spontaneously emitted wave) is incident on the material. Since this wave has
the same frequency as the atomic frequency, there is a finite probability that this wave will force the atom to
undergo the transition 12 EE .
12 EEhf
269
In this case the energy difference between the two levels is emitted in the form of electromagnetic wave that
adds to the incident one. This is the phenomenon of stimulated emission.
There is a fundamental difference between the spontaneous and stimulated emission processes because in
spontaneous emission one photon is emitted and in stimulated emission both incident and emitted photons are
observed.
The rate of such transition is determined by the number of atoms in the excited state 𝑛2 and energy density 𝑢𝑓
of the incident radiation and is given by
funB 221
where B21 is the Einstein’s coefficient for stimulated emission.
Due to the absorption of the electromagnetic radiation, atoms in the lower energy state may make an upward
transition to the higher energy and the rate of such transition is given by
funB 112
Under equilibrium, the numbers of upward and down ward transitions per unit volume and per second are
equal. Therefore, we can write
ff unBunBnA 112221221
From the above equation, we get
1)(
1
2
1
21
1221
21
221112
221
n
n
B
BB
A
nBnB
nAu f
Comparing it with Planck’s radiation formula 1
3
2
exp
18
kT
hffc
hfu
This implies that , 2112 BB and 3
3
21
12 8
c
hf
B
A .
These yields
1
21
1221
21
exp)(
1
kT
hff
B
BB
Au
,
where A and B are Einstein’s coefficients
11.1.2 Laser principle
The principle of operation remains the same though there is a wide range of lasers. Laser action
occurs in three stages: photon absorption, spontaneous emission, and stimulated emission. The
particle of the material, which undergoes the process of excitation, might be an atom, molecule, or
ion depending on the laser material. This principle is based on the principle of stimulated emission of
radiation, the theory that was discussed by Einstein in 1917.The whole concept was discussed in the
previous section.
270
The photon emitted during stimulated emission has the same energy as the incident photon and it is
emitted in the same direction as the latter, thus, getting two coherent photons. If these two coherent
photons are incident on other two atoms in E2, then it will result in emission of two more photons
and hence four coherent photons of the same energy are emitted. The process continues leading to
doubling of the present number of photons
Fig.11. 4 Amplification due to stimulated emission of radiation
If the process is made to go on chain, we ultimately can increase the intensity of coherent radiation
enormously. In figure above, such amplification of the number of the coherent photons due to
stimulated emission is shown.
The necessary condition for this type of amplification of light intensity by stimulated emission of
radiation is that number of atoms in the upper energy state E2 must be sufficiently increased.
Suppose that by some means, such population inversion between the states E2 and E1 has been
achieved in a certain medium so that 12 nn .
ffff cuI ,
where c is velocity of light in the medium
The number of upward induced transition per unit volume is
c
InBunB
f
f 112112
Similarly, the number of downward induced transition c
InBunB
f
f 221221
For each transition the energy ℎ𝑓 is absorbed or emitted so that the rate of change of the energy
density is given by
hfc
InB
c
InBfu
dt
d ff
f )]([)( 112221
Since the light propagate for a distance cdtdx and 1221 BB we get
fff IBnnc
hffI
dx
dfu
dx
dc 2112 )()()(
271
Hence dxdxBf
nn
c
hf
I
dI
f
f
12
12 )(
(i)
Where 1212 )( B
f
nn
c
hf known as the gain constant.
Thus, integrating equation(i) we get
x
fof eII (ii)
Because 𝑛2 was set to be greater than 𝑛1because of population inversion, then 𝛽 will be positive.
Equation ii) shows that 𝐼𝑓 increase as x increases. This means that as the beam of light progress
through a medium its intensity 𝐼𝑓 increases exponentially. Thus, amplification of the beam
From the discussion above, it shows that population inversion is essential criterion for production of
laser
11.1.3 Population inversion
Population inversion: This is the process of increasing excited electrons in higher energy levels.
This is the redistribution of atomic energy levels that takes place in a system so that laser action can
occur.
Fig.11. 5 increase of electrons in excited energy levels
There are different methods of achieving population inversion in atomic states that is essential
requirement to produce laser beam.
Normally, most of the atoms in a medium are in the ground state of energy E0. There are four
different methods of making these atoms to excited states
(i) Excitation with the help of photons. If the atoms are exposed to an electromagnetic radiation of
high frequency, then there is selective absorption of energy and thus atoms are raised to excited
state.
(ii) Excitation by electrons. This method is used in some gas lasers. Electrons are released from the
atoms due to high voltage electric discharge through a gas. These electrons are then accelerated
to high velocities due to high electric field inside a discharge tube. When they collide with
neutral gas atoms, a fraction of these atoms are raised to excited state
eXXe
Where X is an atom in ground state and X is an atom in excited state
272
iii) Inelastic collision between atoms. If a gas contains two different two different kinds of atoms X
and Y, then during electric discharge through the gas some of the atoms are raised to excited state.
iv) Excitation by chemical energy. Sometimes, an atom or a molecule can be a product of a
chemical reaction and can be produced in its excited state. An example is hydrogen combining with
fluorine to form hydrogen fluoride HF that is in excited state.
11.1.4 Laser structure
Activity 11.3
a) From what you know about LASER, what could be the components of laser
b) Are all parts on laser Light Similar? Explain your reasoning.
Fig.11. 6: General structure of Laser
In general case laser system consists of three important parts: Active medium or amplifying
medium, the energy source referred to as the pump or pump source and the optical resonator
consisting of mirrors or system of mirrors.
Pumping Mechanism
Pumping is the process of supplying energy to the laser medium to excite to the upper energy levels.
To have this mechanism, it depends on the existence of interactions between light from pump source
to constituents of active medium. Usually, pump sources can be: electrical discharges, flash lamps,
arc lamps, light from another laser, chemical reactions and even explosive devices. Most common
lasers use electrical or optical pumping. The type of pump source used depends essentially on the
gain medium.
Active Medium
The active medium is the major determining factor of the wavelength of operation, and other
properties of the laser. The gain medium is excited by the pump source to produce a population
inversion, and it is where the spontaneous and stimulated emission of photons take place, leading to
273
the phenomenon of optical gain or amplification. The gain medium may be a solid crystal like a ruby,
a liquid dye, gases like CO2 or He-Ne or semiconductors. The gain medium for some lasers like gas
lasers is closed by a window under the Brewster's angle to allow the beam to leave the laser tube.
Optical resonator or Optical cavity
The optical resonator or optical cavity is a system of two parallel mirrors placed around the gain
medium that provide reflection of the light beam. Light from the medium produced by the
spontaneous emission is reflected by the mirrors back into the medium where it may be amplified by
the stimulated emission. Mirrors are required for most lasers to increase the circulating power within
the cavity to the point where gains exceed losses, and to increase the rate of stimulated emission. One
of the mirrors reflects essentially 100% of the light, while the other less than 100% and transmits the
remainder. Mirrors can be plane, spherical or a combination of both. Here represented are the
common cavities configuration that can be used:
11.1.5 Checking my progress
1. What do you understand by the term LASER?
2. Write in full the acronym L.A.S.E.R
3. In your own words, explain how laser light is produced.
4. Explain the meaning of population inversion and discuss how an atom can be put into excited
state.
274
5.What is the energy of the laser light that propagates with a frequency of 1010 Hz in gaseous
medium. (Given that the plank’s constant sJh 341067.6 )
6.a) What are the three major components of laser?
b) Using diagrams, explain all the types of optical cavity.
275
11.2 PROPERTIES OF LASER LIGHT
Activity 11.4
a) Using the ideas about electromagnetic radiations, what are characteristics of laser light?
b) Do you think all different kinds of laser light have the same properties? Give reasons to support
your answer.
The laser light is not like any other light emitted by usual sources found in nature. This special light
emitted by the laser, has three properties according to its usefulness in many applications:
Coherence, Monochromaticity and Collimation or Directionality.
Fig 1.8Properties of laser light
11.2.1 Coherence
Coherence is the most interesting property of laser light. All photons emitted, are exactly in the same
phase, they are all crest and valley at the same time. It is brought about by the mechanism of the
laser itself in which photons are essentially copied.
The good temporal coherence is essentially for Interferometry like in Holography. Coherence is not
trivial and is brought about by the amplification mechanism of the laser.
11.2.2 Monochromaticity
Monochromaticity is the ability of the laser to produce light that is at one wavelength λ. It is a
requirement for coherence since photons of different wavelengths cannot be coherent. When white
light is dispersed through a prism, you note that it is composed of an infinite number of wavelengths
of light covering the entire visible spectrum as well as into the UV and IR regions. However, no light
source is perfectly monochromatic. Lasers tend to be relatively monochromatic and this depends on
the type of laser. Monochromatic output, or high frequency stability, is of great importance for lasers
being used in Interferometry.
11.2.3 Collimation or Directionality
Collimation or directionality is the property of laser light that allows it to stay in one direction at the
strait line, confined beam for large distances. This property makes it possible to use the laser as a
level in construction or to pinpoint speeders on a highway. This highly directional laser light is
determined by the mechanism of the laser itself.
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Fig.11. 7 Specific direction of laser light
11.2.4 Checking my progress
1. Choose the correct group of terms that are properties of laser light.
A. Coherent, unpolarized, monochromatic, high divergence
B. Monochromatic, low divergence, polarized, coherent
C. Polychromatic, diffuse, coherent, focused
D. Monochromatic, birefringent, nonpolarized, coherent
2. Which of the following properties of laser light enables us to use it to measure distances with great
precision?
A. All the light waves emitted by the laser have the same direction
B. The light waves are coherent
C. The light waves are monochromatic
D. The individual waves effectively work like a single wave with very large amplitude.
3. Explain how coherence, monochromatic and collimation are interconnected.
4. All light in laser light are produced and found to be in the same phase. How does this help in the
formation of 3D images?
5. Laser light can be used as a level. Which special feature that makes it be used as a level. Explain
your answer
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11.3 APPLICATIONS AND DANGERS OF MISUSE OF LASER
11.3.1 Applications of lasers.
Activity 11.5
a) Having studied LASERS, where do you think in real life LASERS are helpful?
b) From your experience, have you ever used LASER light?
c) Other than using it by yourself, what are other places where laser light is applied
There are many interesting uses for lasers, depending on the special characteristic being applied.
Laser Diodes are used in a wide range of applications. Partial lists of those applications include:
(i) They are used in common consumer devices such as DVD players, bar code scanners; CD
ROM drivers; laser disc and other optical storage drivers; laser printers and laser fax machines;
sighting and alignment scopes; measurement equipment; free space communication systems;
pump source for other lasers; high performance imagers; and typesetters. CD players have
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lasers. Light from the laser in CD player reflects off patterns on CD’s surface. The reflected
light is converted to a sound wave.
(ii) Laser beams can be used in diverse fields of science and technology. Like in the control of
motion of moving objects like aircrafts or missiles. This method thus makes it possible for a
missile to hit a certain target.
(iii) Because of high directional property, lasers are used to measure distances accurately. A laser
beam is sent and the time taken for it to be reflected back is measured. Using this idea, the
distance can thus be measured.
(iv) Because laser beam can be focused into a small spot, it can thus be used to cut minute holes onto
a material.
(v) The very high intensity of laser beam means that the amplitude of the corresponding
electromagnetic wave is very large. So it is possible to investigate the non linear optical
properties of different materials with the help of laser light.
(vi) Lasers are also used in industry for cutting materials such as metal and cloths. and welding
materials
(vii) Doctors use lasers for surgery and various skin treatments
(viii) They are used in military and law enforcement devices for marking targets and measuring
range and speed.
(ix) Laser lighting displays use laser light as an entertainment medium.
(x) Lasers also have many important applications in scientific research
In a tabular way, we can have a summary of different types of lasers and their applications.
The following are types of lasers and their Applications
a) Gas Lasers:
Laser
Gain
Medium
Operation
Wavelength(s) Pump Source Applications
Helium-
neon laser 632.8 nm Electrical discharge
Holography, spectroscopy,
barcode scanning, alignment,
optical demonstrations
Argon
laser
454.6 nm, 488.0 nm,
514.5 nm Electrical discharge
Retinal phototherapy (for
diabetes), lithography, confocal
microscopy, spectroscopy
pumping other lasers
Carbon
dioxide
laser
10.6 μm, (9.4 μm) Electrical discharge Material processing (cutting,
welding, etc.), surgery
Excimer
laser
193 nm (ArF), 248 nm
(KrF), 308 nm (XeCl),
353 nm (XeF)
Excimer
recombination via
electrical discharge
Ultraviolet lithography for
semiconductor manufacturing,
laser surgery
Table.11. 1 Gas lasers and their applications
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b) Solid State Lasers:
Laser Gain
Medium
Operation
Wavelength(s)
Pump
Source Applications
Ruby laser 694.3nm Flash Lamp Holography, tattoo removal. The first type
of visible light laser invented; May 1960.
Nd:YAG laser 1.064 μm, (1.32 μm) Flash Lamp,
Laser Diode
Material processing, laser target
designation, surgery, research, pumping
other lasers. One of the most common high
power lasers.
Erbium doped
glass lasers 1.53-1.56 μm Laser diode
um doped fibers are commonly used as
optical amplifiers for telecommunications.
F-center laser Mid infrared to far
infrared
Electrical
current Research purposes.
Table.11. 2 Solid state lasers characteristics and their applications.
c) Metal-vapor Lasers:
Laser Gain
Medium
Operation
Wavelength(s) Pump Source Applications
Helium-cadmium
(HeCd) metal-
vapor laser
441.563 nm,
325 nm
Electrical discharge in
metal vapor mixed with
helium buffer gas.
Printing and typesetting
applications, fluorescence
excitation examination
Copper vapor
laser
510.6 nm,
578.2 nm Electrical discharge
Dermatological uses, high
speed photography, pump for
dye lasers
Table.11. 3 Metal-vapor lasers characteristics and their applications
d) Other types of lasers:
Laser Gain
Medium Operation Wavelength(s) Pump Source Applications
Dye lasers Depending on materials,
usually a broad spectrum
Other laser,
flash lamp
Research, spectroscopy,
birthmark removal, isotope
separation.
Free electron
laser
A broad wavelength range
(about 100 nm - several mm)
Relativistic
electron beam
Atmospheric research,
material science, medical
applications
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Table.11. 4 Other kinds of lasers characteristics and their applications
11.3.2 Dangers of lasers
ACTIVITY 11.6
a) Laser light is used in many areas like industries, offices, airports and many other places. Do you
think long exposure of laser light is harmful?
b) Why do you think so?
c) What makes these lasers harmful if mis-used? Give a scientific reasoning
You should be careful when dealing with lasers, because they can have a negative impact when
exposed to your body. Among other negative effects, some of them are discussed below
i. If directly exposed to our skin, it burns the skin
ii. When absorbed by skin, Laser light reacts with body cells causing cancer.
iii. Because of their high energy, it affects eyes if exposed to them
iv. Lasers can affect cells of a human being. This leads to mutation
Because of the negative effects of lasers, care must be taken to avoid all the risks of being affected
by lasers.
11.3.3 Precaution measures to avoid negative effects of lasers
Activity 11.7
a) Observe the picture above clearly. Using scientific reasoning explain why the people
performing the activity above are putting on protective wear as shown.
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b) Building on what you have discussed in a) above, what precautional measures can you take to
avoid negative effects of LASERS if at all you were working in a place exposed to them.
The following are some of the measures one can take to avoid the negative effects of lasers.
i) For any one working in places where there are incidences of being exposed to laser light, one
should wear protective clothes, glasses and shoes so that there is no direct exposure of these
radiations on to the body.
ii) One should minimize the time of working with lasers.
iii) Areas that are exposed to these radiations should be warning signs and labels so that one can be
aware of places/areas where laser light is used.
iv) Safe measures like Use of remote control should be used to avoid direct exposure of these
radiations (LASER light).
v) People should be given trainings on how to handle lasers.
vi) There should also access restrictions to laboratories that use laser
11.3.4 Checking my progress
1. Discuss all the negative effects of laser light.
2. Using vivid examples, explain how one can prevent him or herself of all dangers caused by laser
light.
3. We have seen that laser light is good and at the same time bad. Using your personal judgement,
which side outweighs the other. Give scientific reasons.
4. Depending on your judgement in (3) do you think man should continue using laser light?
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11.4 END UNIT ASSESSMENT
11.4.1 Multiple choice
Copy the questions below to your exercise and chose the best alternative that answers the question.
1) What does the acronym LASER stand for?
A. Light Absorption by Stimulated Emission of Radiation
B. Light Amplification by Stimulated Emission of Radiation
C. Light Alteration by Stimulated Emission of Radiation
2) The acronym MASER stands for?
A. Microwave Amplification by Stimulated Emission of Radiation
B. Molecular Absorption by Stimulated Emission of Radiation
C. Molecular Alteration by Stimulated Emission of Radiation
D. Microwave amplification by Stimulated Emission of Radio waves
3) What is one way to describe a Photon?
A. Solid as a rock
B. A wave packet
C. A torpedo
D. Electromagnetic wave of zero energy
4) Which of the following determines the color of light?
A. its intensity
B. its wavelength
C. its source
D. Some information missing
5) Among the three examples of laser listed below, which one is considered “eye safe”?
A. Laser bar-code scanners
B. The excimer laser
C. Communications lasers
D. YAG
6) Why are lasers used in fiber optic communications systems
A. The government has mandated it
B. They can be pulsed with high speed data
C. They are very inexpensive
D. They are not harmful
7) Lasers are used in CDs and DVDs. What type of laser is used in these players?
A. Semiconductor
B. YAG
C. Alexandrite
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D. All the above
8) The best reason why lasers used in “Laser Printers” is
A. They can be focused down to very small spot sizes for high resolution
B. They are cheap
C. They are impossible to damage
D. They are locally available
9) As wavelength gets longer, the laser light can be focused to…
A. Larger spot sizes
B. Smaller spot sizes
C. Large and small spot sizes
D. None of the above
10) Among the following, which color of laser has the shortest wavelength?
A. Yellow C. Blue
B. Red D. Green
11) What property of laser light is used to measure strain in roadways?
A. Intensity
B. Power
C. Coherence
D. All the above
12) What is the type of laser used most widely in industrial materials processing applications?
A. Dye Laser B. YAG laser
B. Ruby Laser D. Carbon Dioxide Laser
13) Why are lasers used for cutting materials
A. It never gets dull D. It has a small “heat affected zone”
B. Accuracy E. Smoother cuts
C. Repeatability F. All of the above
14) The Excimer laser produces light with what wavelength?
A. Visible
B. Ultraviolet
C. Infrared
D. All the above.
15) Most lasers are electrically inefficient devices.
A. True
B. False
16) Chemical lasers use………………. to produce their beams.
A. Excessive amounts of electrical power
B. Small amounts of electrical power
C. No electrical power
D. Other lasers
17) What type of laser could cause skin cancer if not used properly?
A. Red semiconductor laser C. Blue semiconductor
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B. Excimer laser D. YAG laser.
11.4.2 Structured questions
18a) What do you understand by term LASER?
b) Depending on the nature and what laser is made of, Laser is classified into different types. Discuss
at least 5 types of lasers
19. The following are basic characteristics of laser light. With clear explanation, what does each
imply as connected to laser light.
a. Coherence
b. Monochromaticity
c. Collimation
20)a) With the aid of diagram Explain the meaning of the following terms
(i) Spontaneous Absorption of light
(ii) Stimulated Emission
(iii)Spontaneous Emission
(iv) Population inversion
b) Laser light have been employed in different areas. This has helped man in solving different
problems. What are some of the areas where laser light is employed.
c) Though laser light is very important in different activities, it can also cause harm if mis-used In
what ways is laser light harmful.
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UNIT 12: MEDICAL IMAGING
Key unit Competence:
By the end of the unit the learner should be able to analyze the processes in medical imaging.
Learning objectives:
Outline specific purposes of imaging techniques
Explain the effects of various imaging techniques for particular purposes.
Explain the basic functioning principles of major medical imaging techniques
Identify advantages and disadvantages of medical imaging techniques
INTRODUCTORY ACTIVITY:
Investigation on the use of medical imaging techniques:
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fig.12. 1: Medical imaging techniques
Years ago, the only way to get information from inside of human bodies was through surgery.
In modern medicine, medical imaging has undergone major advancements and this ability to
obtain information about different parts of the human body has many useful clinical
applications.
Using information provided on the above pictures, answer to the following questions:
1. Observe the image A, B, and C (Fig.12.1) and describe what is happening.
2. Suggest the technique that is being used for each image?
3. Explain the working principle of the mentioned techniques in question 2?
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12.1 X-RAY IMAGING.
12.1.1 Interaction of X-rays with matter.
a- Introduction
In unit 10, we learnt that X-rays are electromagnetic radiation produced by focusing a beam
of high energy electron on a target material in x-ray tube. Since the major part of the energy
of the electrons is converted into heat in the target (only about 1% will appear as X-rays), the
target material should have a high melting point and good heat conduction ability. To get a
high relative amount of X-ray energy, the anode material should be of high atomic number.
Tungsten is the dominating anode material and is in modern X-ray tubes often mixed with
Rhenium.
In X-ray diagnostics, radiation that is partly transmitted through and partly absorbed in the
irradiated object is utilized. An X-ray image shows the variations in transmission caused by
structures in the object of varying thickness, density or atomic composition.
Fig.12.2: The necessary attributes for X-ray imaging are shown: X-ray source, object
(patient) and a radiation detector (image receptor).
Activity 12.1: Exploration of x-ray image
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Analyze the figure below answer to the following questions:
Fig.12.3 procedure of X-ray image formation
1. What do the letters A, B, C, D and E stand for?
2. Explain the process used from A to E.
3. Explain how radiology differ from radiography.
b) Attenuation and Absorption of X-rays
There are principally two interaction processes that give rise to the x-ray attenuation
(variation in photon transmission) through the patient which is the basis of X-ray imaging.
These are photoelectric absorption and scattering processes.
Fig.12.4: Attenuation of monoenergetic X-ray photons in a thin layer of a given material
A photon which has experienced an interaction process has either been absorbed or has
changed its energy and/or direction of motion. A photon that changes its direction of motion
is called a scattered photon. For monoenergetic x-ray photons, the number of photons that
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experience such interactions and therefore removed from the primary beam when this is
incident on a thin layer of material is proportional to the number of incident photons (N) and
the thickness of the layer (dx) following the expression :
dN = −μNdx 12.01
where µ is a constant of proportionality called the linear attenuation coefficient. Integrating
the above equation will result in
N(x) = 𝑁𝑜 exp(−μx) , 12.02
where 𝑁𝑜 is the initial number of photons in the incident beam.
It can be seen that the incident beam photons (or the beam energy) is attenuated exponentially
as the X-rays travel through the material. The different interaction processes involved, that
are absorption, coherent and incoherent scattering and pair production, add their contributions
to the total linear attenuation coefficient
μ = μa + μcoh + μincoh + μp 12.03
where µa, µcoh, µincoh, and µp are the contributions to the attenuation from photoelectric
absorption, coherent scattering, incoherent scattering and pair production.
c) Contrast
The contrast is a measure of the difference in radiation transmission or other
parameters between
two adjacent areas in a radiographic image. Contrast plays an important role in the ability of a
radiologist to perceive image detail.
Fig. 12.5: Illustration of the concept of contrast.
The contrast C, can be estimated as
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c =ε1−ε2
ε1 12.04
where ε1 and ε2 are energies of the monoenergetic X-ray photons per unit area reaching the
detector and therefore absorbed in the detector without and with the contrasting detail
respectively. In the case where the film is used as image receptor, the signal is obtained in
terms of the optical density. The image contrast is then usually defined as the optical density
difference beside and behind the contrasting detail.
In such situation where monoenergetic photons are considered and no scattered radiation is
reaching the detector, the absorbed energy in the detector can be written as
ϵ1 = ε0 exp(− μ1 d) 12.05
Where d, is the thickness of the object with linear attenuation coefficient μ1
The energy through the contrasting detail can be expressed as
ϵ2 = ε0exp(−μ1(d − x)) . exp(−μ2x) 12.06
where ε0 is the energy absorbed in the detector with no object present, x is the thickness of
the contrasting detail with its linear attenuation coefficient µ2.
Replacing equation 12.05 and 12.06 into equation 12.04 we obtain the contrast c as,
c =ε1−ε2
ε1= 1 − exp (−(μ2 − μ1)x) 12.07
Expanding exp (−(μ2 − μ1)x), for small values of x, reduces to
c = (μ2 − μ1)x 12.08
The contrast is then proportional to the difference in the linear attenuation coefficients and
the thickness of the contrasting detail. Therefore, when scattered radiation is neglected in the
process, the contrast is independent of the thickness d of the object but also it does not
depend on where in the object the contrasting detail is situated.
The ability of conventional radiography to display a range of organs and structures may be
enhanced by the use of various contrast materials, also known as contrast media. The most
common contrast materials are based on barium or iodine. Barium and iodine are high atomic
number materials that strongly absorb X-rays and are therefore seen as dense white on
radiography.
12.1.2 X-rays Imaging Techniques
a) Conventional Radiography
X-rays are able to pass through the human body and produce an image of internal structures.
The resulting image is called a radiograph, more commonly known as an ‘X-ray’ or ‘plain
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film’. The common terms ‘chest X-ray’ and ‘abdomen X-ray’ are widely accepted and
abbreviated to CXR and AXR.
As a beam of X-rays passes through the human body, some of the X-rays photons are
absorbed or scattered producing reduction or attenuation of the beam with the internal human
structure acting as contrasting details. Therefore tissues of high density and/or high atomic
number cause more X-ray beam attenuation and are shown as lighter grey or white on
radiographs. Less dense tissues and structures cause less attenuation of the X-ray beam, and
appear darker on radiographs than tissues of higher density. The figure below shows the
typical conventional radiograph of a human body.
Fig.12.6: The five principal radiographic densities. This radiograph of a benign lipoma
(arrows) in a child’s thigh demonstrates the five basic radiographic densities: (1) air; (2)
fat; (3) soft tissue; (4) bone; (5) metal. (David A Disle (2012) Imaging for students.
Fourth Edition. (Page 1))
Five principal densities are easily recognized on this plain radiograph due to the increase in
their densities:
1. Air/gas appears as black, e.g. lungs, bowel and stomach
2. Fat is shown by dark grey, e.g. subcutaneous tissue layer, retroperitoneal fat
3. Soft tissues/water appears as light grey, e.g. solid organs, heart, blood vessels, muscle and
fluid-filled organs such as bladder
4. Bone appears as off-white
5. Contrast material/metal: bright white.
In the past, X-ray films were processed in a darkroom or in freestanding daylight processors.
In modern practice, radiographic images are produced digitally using one of two processes,
computed radiography (CR) and digital radiography (DR).
DR uses a detector screen containing silicon detectors that produce an electrical signal when
exposed to X-rays. This signal is analyzed to produce a digital image. Digital images
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obtained by CR and DR are sent to viewing workstations for interpretation. Images may also
be recorded on X-ray film for portability and remote viewing.
Fig.12.7: Computer radiography image.
The image given by a computer radiography may be reviewed and reported on a computer
workstation. This allows various manipulations of images as well as application of functions such as
measurements of length and angles measurements.
The relative variance of the shadows depends upon the density of the materials within the
object or body part. Dense, calcium – rich bone absorbs X-rays to a higher degree than soft
tissues that permit more X-rays to pass through them, making X-rays very useful for
capturing images of bone.
In projection radiography, there is much room for adjusting the energy level of the X-rays
depending on the relative densities of the tissues being imaged and also how deep through a
body the waves must travel in order to achieve the imaging.
Images of bones (for instance, to examine a fracture or for diagnostic measures related to
bone conditions like osteoarthritis or certain cancers) require high-energy X-rays because of
the high density of bone.
Images of soft tissues like lungs, heart and breasts (both chest X-rays and mammography are
very common diagnostic applications of X-rays) require relatively less energy from the X-
rays in order to penetrate properly and achieve excellent images.
In order to achieve these different energies, technologists use X-ray generators of different
voltages and equipped with anodes made of different metals.
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B. MAMMOGRAPHY
ACTIVITY 12.2
One day a girl suffering from the breast tells her mother about the problem. And her mother advises
her to go to the hospital to consult a doctor.
(a) Think of the problem that girl may have.
(b) Try to explain what may be the cause of that problem.
(c) If you are a doctor how can you detect such problem?
(d) Which advise can you give to other people who are not suffering from that problem in order to prevent it?
Mammography is a specialized medical imaging that uses low-dose X-rays to investigate the
internal structure of the breast. A mammography exam, called a mammogram, helps in the
early detection and diagnosis of women’s breast diseases such as breast cancer before even
experiencing any symptom. Below is a typical mammography test showing the presence of
abnormal areas of density, mass, or calcification that may indicate the presence of cancer.
fig.12. 8: Mammography:(a) the breast is pressed between two plates x-rays are used to takes
pictures of breast tissues,(b)photographic image of breast tissues, (c)Breast with cancer.
A mammography unit is a rectangular box that houses the tube in which X-rays are produced.
The unit is used exclusively for X-ray exams of the breast, with special accessories that allow
only the breast to be exposed to the X-rays. Attached to the unit is a device that holds and
compresses the breast and positions it so images can be obtained at different angles.
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In conventional film and digital mammography, a stationery X-ray tube captures an image from
the side and an image from above the compressed breast. Breast tomosynthesis, also called three-
dimensional (3-D) mammography and digital breast tomosynthesis (DBT), is an advanced form of
breast imaging where multiple images of the breast from different angles are captured and
reconstructed ("synthesized") into a three-dimensional image set. In this way, 3-D breast imaging is
similar to computed tomography (CT) imaging in which a series of thin "slices" are assembled
together to create a 3-D reconstruction of the body.
C. COMPUTER TOMOGRAPHY SCAN (CT SCAN)
a) CT terminology
In 1970s, a revolutionary new X-ray technique was developed called Computer tomography
(CT), which produce an image of a slice through the body. The word tomography comes from
the Greek: tomos =slice, graph= picture.)
A computed tomography scan also known as CT scan, makes use of computer-processed
combinations of many X-ray measurements taken from different angles to produce cross-
sectional (tomographic) images (virtual "slices") of specific areas of a scanned object,
allowing the user to see inside the object without cutting it. Other terms include computed
axial tomography (CAT scan) and computer aided tomography
The term "computed tomography" (CT) is often used to refer to X-ray CT, because it is the
most commonly known form but many other types of CT exist.
CT is an imaging technique whereby cross-sectional images are obtained with the use of X-
rays. In CT scanning, the patient is passed through a rotating gantry that has an X-ray tube on
one side and a set of detectors on the other. Information from the detectors is analysed by
computer and displayed as a grey-scale image. Owing to the use of computer analysis, a
much greater array of densities can be displayed than on conventional X-ray films. This
allows accurate display of cross-sectional anatomy, differentiation of organs and pathology,
and sensitivity to the presence of specific materials such as fat or calcium. As with plain
radiography, high- density objects cause more attenuation of the X-ray beam and are
therefore displayed as lighter grey than objects of lower density.
b) Principle behind of computer tomography scan (CT scan).
Computer Tomography is shown in below figure: a thin collimated beam of X- ray (“ to
collimate” means to “make straight”) passes through the body to a detector that measures the
transmitted intensity. Measurements are made at a large number of points as the source and
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detector are moved past the body together. The apparatus is rotated slightly about the body
axis and again scanned; this is repeated at intervals for . The intensity of the
transmitted beam for the many points of each scan, and for each angles, are sent to a
computer that reconstructs the image of the slice. Note that the imaged slice is perpendicular
to the long axis of the body. For this reason, CT is sometimes called computerize axial
tomography.
Fig.12. 9: Tomography image
The use of single detector would require a few minutes for many scans needed to form a
complete image. Much faster scanner use a fan beam in which passing through the entire
cross section of the body are detected simultaneously by many detectors.The x-ray source and
the detectors are rotated about the patient and an image requires only few seconds to be seen.
This means that rays transmitted through the entire body are measured simultaneously at each
angle where the source and detector rotate to take measurements at different angles.
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Fig.12. 10: computer tomography scan
CT images of internal organs, bones, soft tissue, and blood vessels provide greater clarity and
more details than conventional X-ray images, such as a chest X-Ray.
Function of CT scan
A motorized table moves the patient through a circular opening in the CT imaging system.
While the patient is inside the opening, an X-ray source and a detector assembly within
the system rotate around the patient. A single rotation typically takes a second or less. During
rotation the X-ray source produces a narrow, fan-shaped beam of X-rays that passes through a
section of the patient's body.
Detectors in rows opposite the X-ray source register the X-rays that pass through the patient's
body as a snapshot in the process of creating an image. Many different "snapshots" (at many
angles through the patient) are collected during one complete rotation.
For each rotation of the X-ray source and detector assembly, the image data are sent to a
computer to reconstruct all of the individual "snapshots" into one or multiple cross-sectional
images (slices) of the internal organs and tissues.
Note that, it is advisable to avoid unnecessary radiation exposure; a medically needed CT
scan obtained with appropriate acquisition parameter has benefits that outweigh the radiation
risks.
12.1.3 Checking my progress
1. Outline the advantage and disadvantages CT scan
2. Explain the types of x-ray imaging used in mammography.
3. In mammography exams, is the breast compression necessary? Why
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4. A beam of X-rays passes through the human body of tissues with different densities;
explain the production of X-rays on less dense tissues?
12.2 ULTRASONIC IMAGING
12.2.1 Basics of Ultra sound and its production
ACTIVITY 12.3
1. Distinguish ultrasound from infrasound?
2. Where do you think ultrasound may be applied in daily life?
3.Advise on how ultrasound be used in medicine?
Sound can refer to either an auditory sensation in the brain or the disturbance in a medium
that causes this sensation. Hearing is the process by which the ear transforms sound
vibrations into nerve impulses that are delivered to the brain and interpreted as sounds. Sound
waves are produced when vibrating objects produce pressure pulses of vibrating air. The
auditory system can distinguish different subjective aspects of a sound, such as its loudness
and pitch.
Pitch is the subjective perception of the frequency, which in turn is measured in cycles per
second, or Hertz (Hz). The normal human audible range extends from about 20 Hz to
20 000 Hz, but the human ear is most sensitive to frequencies of 1 000 Hz to 4 000 Hz.
Loudness is the perception of the intensity of sound, related to the pressure produced by
sound waves on the tympanic membrane. The pressure level of sound is measured in decibels
(dB), a unit for comparing the intensity of a given sound with a sound that is just perceptible
to the normal human ear at a frequency in the range to which the ear is most sensitive. On the
decibel scale, the range of human hearing extends from 0 dB, which represents the auditory
threshold, to about 130 dB, the level at which sound becomes painful.
12.2.2 Interaction of sound waves with different structure inside the body
a- Introduction
Ultrasound imaging uses ultra-high-frequency sound waves to produce cross-sectional images
of the body. Ultrasound is actually sound with a frequency in excess of 20 kHz, which is the
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upper limit of human hearing. Typical ultrasound frequencies used for clinical purposes are in
the 2 MHz to 10 MHz range.
Different tissues in a human or animal body alter the ultra sound waves in different ways.
Some waves are reflected directly while others scatter the waves before they return to the
transducer as echoes. The reflected ultrasound pulses detected by the transducer need to be
amplified in the scanner or ultrasonic probe. The echoes that come from deep within the body
are more attenuated than those from the more superficial parts and therefore required more
amplification. When echoes return to the transducer, it is possible to reconstruct a two
dimensional map of all the tissues that have been in the beams. The information is stored in a
computer and displayed on a video (television) monitor. Strong echoes are said to be of the
high intensity and appear as brighter dots on the screen.
b- Reflection of ultrasound
When the pulse of ultrasound is sent into the body and meets a boundary between two media,
of different specific acoustic impedance Z, the sound wave needs to change gear in order to
continue. If the difference in Z across the boundary is large the wave cannot easily adjust:
there is an “acoustic mismatch”. Most of the wave is reflected and a strong echo is recorded.
The fraction of intensity reflected back (Ir) to that incident (Ir) at the normal incidence, is
known as the intensity of reflection coefficient α
α =Ir
Ii (12.09)
which in turn reduces deduces to;
(12.10)
where 𝑍is acoustic impedance
Note that large difference in Z give rise to large values for α, producing strong echoes
Example 12.4
1. Estimate the percentage of incidence intensity reflected back at fat per muscle
boundary.
Answer:
we need to calculate the value of α for the boundary using the equation
with Z1 = 1.38 X106kgm−2s−1and Z2 = 1.70 X106kgm−2s−1
2
12
2
12
)(
)(
ZZ
ZZ
2
12
2
12
)(
)(
ZZ
ZZ
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Hence, 1.1% of the incidence intensity is reflected back.
Ultrasounds are high-frequency sound waves above the human ear’s audible range: that is
with frequency sound waves greater than 20 kHz. In fact, the frequencies used in medicine
are much higher than this, typically between 1 MHz and 15 MHz. like all sound waves,
ultrasound consists of longitudinal, elastic or pressure waves, capable of traveling through
solids, liquids and gases. This makes them ideal for penetrating the body, unlike transverse
mechanical waves, which cannot travel to any great extent through fluids.
c- Attenuation of ultrasound
The attenuation of the waves describes the reduction in its intensity as they travel through a
medium. This loss is due to a number of factors:
The wave simply “spreads out” and suffers an “inverse square law type” reduction in intensity.
The wave is scattered away from its original direction
The wave is absorbed in the medium.
The amount of absorption of ultrasound beam in a medium is described by the absorption
coefficient , which is intensity level per unit length. It is expressed in decibels per cm and it
firstly depends on the type of medium the wave is propagating into. As example whilst water
absorbs very little ultrasound, bone is a strong absorber, putting it at risk, for example, during
high- power ultrasound therapy.
Secondly, higher frequencies suffer greater absorption. In fact if the frequency is doubled, the
absorption increases by the factor of four. This has very important consequences when
choosing the best frequency at which to image the body. If the selected frequency is too high,
the ultrasound will not be able to penetrate to the regions under investigation.
12.2.3 Ultrasonic imaging techniques
The basic component of the ultrasound probe is the piezoelectric crystal. Excitation of this
crystal by electrical signals causes it to emit ultra-high-frequency sound waves; this is the
piezoelectric effect. The emitted ultrasound waves are reflected back to the crystal by the
various tissues of the body. These reflected sound waves also called the “echoes” act on the
011.0)38.170.1(
)38.170.1(2
2
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piezoelectric crystal in the ultrasound probe to produce an electric signal, again by the
piezoelectric effect. It is this electric signal which is analysed by a computer produces a
cross-sectional image.
Fig.12.11: Typical set up of ultrasound system
The process of imaging is the same as the echo-locating sonar of a submarine or a bat. The
observer sends out a brief pulse of ultrasound and waits for an echo. The pulse travels out,
reflects off the target and returns. The ultrasound machine uses pulses because the same
device acts as both transmitter and receiver. If it continually sent out sounds, then the receiver
would not hear the much softer echo over the louder transmission.
The duty cycle of the ultrasound imager is the amount of time spent transmitting compared to
the total time of transmitting and listening.
Sonar is an acronym for Sound Navigation and Ranging. It relies on the reflection of
ultrasound pulses. A short pulse of ultrasound is directed towards the object interest, which
then reflects it back as an echo. The total time t between transmission of pulse and reception
of an echo is measured, often using a cathode ray oscilloscope (CRO). The sonar principle
is used to estimate the depth of a structure, using
, (12.11)
where t is the time taken to go and back and 𝑣 is the velocity of ultrasound in the medium.
The factor of 2 is necessary because the pulse must travel “there and back”
An ultrasound beam structure is directly into the body. The reflection or echoes from
different body structure are then detected and analyzed, yielding information about the
locations. For example if the time delays between the reception of echo pulse1 and 2
2
vtd
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(Fig.12.7 below) is t, then the diameter of the baby’s head can be found using the above
formula.
Fig.12. 12: Echo location: (a) conventional sonar; (b) medical imaging
Example 12.4
During an investigation using ultrasound, the time delay for an echo to return from a
structureis 10.5𝜇𝑠. If the average velocity of ultrasound in the eye is 1510 m/s. Calculate the
depth of the structure.
𝑑 =1510𝑚𝑠−1𝑥10.5𝑥10−6𝑠
2= 7.93𝑥10−3𝑚 = 7.93𝑚𝑚
c) Doppler ultrasonic
An object travelling towards the listener causes sound waves to be compressed giving a
higher frequency; an object travelling away from the listener gives a lower frequency. The
Doppler effect has been applied to ultrasound imaging. Flowing blood causes an alteration to
the frequency of sound waves returning to the ultra sound probe. This frequency change or
shift is calculated allowing quantization of blood flow. The combination of conventional two-
dimensional ultra sound imaging with Doppler ultra sound is known as Duplex ultra sound.
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Fig.12.11: Duplex ultra sound. The Doppler sample gate is positioned in the artery (arrow) and
the frequency shifts displayed as a graph. Peak systolic and end diastolic velocities are
calculated and also displayed on the image in centimeters per second.
As ultrasound imaging uses sound waves to produce pictures of inside of the body. It is used
to help diagnose the cause of pain, swelling and infection in the body’s internal organs and to
examine a baby in pregnant woman and the brain and hips in infants. It is also used to help
guide biopsies, diagnose heart conditions and assess damage after a heart attack.
Ultrasound examinations do not use ionizing radiation (x-rays), there is no radiation exposure
to the patient. Because ultrasound image are captured in real time, they can show the structure
and movement of the body’s internal organs, as well as blood flowing through blood vessels.
d) Advantages and Disadvantages of ultrasounds
The advantages of ultrasound over other imaging modalities include:
• Lack of ionizing radiation.
• Relatively low cost
• It is noninvasive (of medicine procedures not involving the introduction of instruments into the
body)
• Quick procedure
• Good for examining soft tissues.
• Portability of equipment.
Some disadvantages of ultrasound include:
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It is highly operator dependent as it relies on the operator to produce and interpret images at
the time of examination
Not as much details as X-rays and MRI
It cannot be used in areas that contain gas (such as lungs)
Doesn’t pass through bones.
Can be wrong in detecting physical abnormalities.
12.2.4 Checking my progress
1.Explain how ultrasound imaging is used?
2. Who take the decision to scan or not to scan in normal pregnancy?
3. What are the risks and side effects to the mother or baby during ultrasound?
4. If an ultrasound is done at 6 to 7 weeks and a heartbeat is not detected, does that mean
there is a problem?
12.3 SCINTIGRAPHY (NUCLEAR MEDICINE)
Activity 12.4
a) What do you understand by ‘radionuclide imaging’?
b) What is a radionuclide scan used for?
c) Compare radionuclide scan with mammography scan?
12.3.1 Physics of scintigraphy and terminology
Scintigraphy refers to the use of gamma radiation to form images following the injection of
various radiopharmaceuticals. The key word to understanding of scintigraphy is
radiopharmaceutical. ‘Radio’ refers to the radionuclide, i.e. the emitter of gamma rays.
The most commonly used radionuclide in clinical practice is technetium, written in this text
as , where 99 is the atomic mass, and the ‘m’ stands for metastable. Metastable means
that the technetium atom has two basic energy states: high and low energy states. As the
technetium transforms from the high-energy state to the low-energy state, it emits a quantum
of energy in the form of a gamma ray, which has energy of 140 keV. Other commonly used
mTc99
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radionuclides include gallium citrate ( ), thallium ( ), indium ( ) and iodine (
).
Fig.12.1 2: Gamma ray production. The metastable atom passes from a high-energy to a
low-energy state and releases gamma radiation with a peak energy of 140 keV.
12.3.2 Basic functioning of radionuclide scan
Activity12.6
For radionuclide imaging, it is advisable for the patient to consume a small quantity of
radionuclide, or it is injected into a vein in your arm.
a) How long does it take?
b) What is the purpose of those radionuclide chemicals?
(c) Assuming the patient has already consumed the radionuclide for him/her to be scanned
and wants to take another scan on another part of the body, will the patient be required to take
another dose of the nuclide?
d) You as a student, what advice can you give to a patient who develops allergies after taking
the radio nuclear chemical?
A radionuclide scan is a way of imaging bones, organs and other parts of the body by using
a small dose of a radioactive chemical. There are different types of radionuclide chemical.
The one used depends on which organ or part of the body need to be scanned.
A radionuclide (sometimes called a radioisotope or isotope) is a chemical which emits a type
of radioactivity called gamma rays. A tiny amount of radionuclide is put into the body,
usually by an injection into a vein. Sometimes it is breathed in, or swallowed, or given as eye
drops, depending on the test.
Gamma rays are similar to X-rays and are detected by a device called a gamma camera. The
gamma rays which are emitted from inside the body are detected by the gamma camera, are
Ga67TI201 In111
I131
mTc99
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converted into an electrical signal and sent to a computer. The computer builds a picture by
converting the differing intensities of radioactivity emitted into different colors or shades of
grey.
However, radionuclide imaging techniques do not depict structural anatomy like ultrasound,
X-ray computed tomography (XCT) or conventional radiographs. It is the only established
noninvasive technique available to investigate organ physiology, although recently Nuclear
magnetic resonance (NMR) imaging technique has shown its capability to probe organ
physiology and anatomy without ionizing radiation.
Radionuclide scans do not generally cause any after effects. Through the natural process of
radioactive decay, the small amount of radioactive chemical in your body will lose its
radioactivity over time. Although the levels of radiation used in the scan are small, patients
may be advised to observe special precautions.
12.3.3 Limitations and disadvantages of scintigraphy
The main advantages of scintigraphy are its high sensitivity and the fact that the functional
information is provided as well as anatomical information. However it has some
disadvantages that are listed below:
i. Generally poor resolution compared with other imaging techniques.
ii. Radiation risks due to the administered radionuclide
iii. Can be invasive, sometimes requiring an injection into the bloodstream
iv. Disposal for radioactive waste, including that from patients, requires special procedures.
v. Relatively high costs associated with radiotracer production and administration.
12.3.4 Checking my progress
Choose the correct answers
1. Scintigraphy refers to the use of:
a) Gamma radiation to form images
b) X- ray radiation to form images
c) X- rays and gamma radiations to form images
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d) None of radiation to form images.
2. The radionuclide in clinical practice are
a) Technetium
d) Thallium
c) Gallium
d) ALL of them
12.4 MAGNETIC RESONANCE IMAGING (MRI)
Activity 12.7: Principles of MRI
i) What does MRI mean?
ii) What is it used for?
iii) What makes MRI to be powerful compared to other imaging techniques?
iv) is it advisable for a pregnant woman to be placed in MRI Scanner? Explain your view?
12.4.1. MRI physics and terminology.
Magnetic resonance (MR) imaging has become the dominant clinical imaging modality with
widespread, primarily noninvasive, applicability throughout the body and across many
disease processes. The progress of MR imaging has been rapid compared with other imaging
technologies and it can be attributed in part to physics and in part to the timing of the
development of MR imaging, which corresponded to an important period of advances in
computing technology.
Initially let us described how magnetic resonance can be demonstrated with a pair of magnets
and a compass. If a compass happens to find itself near a powerful magnet, the compass
needle will align with the field. In a normal pocket compass, the needle is embedded in liquid
to dampen its oscillations. Without liquid, the needle will vibrate through the north direction
for a period before coming to rest. The frequency of the oscillations depends on the magnetic
field and of the strength of the magnetic needle.
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Figure 12.15: small coil placed to the magnetic needle
Let us focus on what made the needle oscillate. It was the small movements of the magnet,
back and forth, or more precisely the oscillation of a weak magnetic field perpendicular to the
powerful stationary magnetic field caused by the movement of the magnet. But oscillating
magnetic field is what we understand by “radio waves”, which means that in reality, we could
replace the weak magnet with other types of radio wave emitters. This could, for example, be
a small coil subject to an alternating current, as shown in figure above. Such a coil will create
a magnetic field perpendicular to the magnetic needle. The field changes direction in
synchrony with the oscillation of the alternating current, so if the frequency of the current is
adjusted to the resonance frequency of the magnetic needle, the current will set the needle in
motion. This is also applied in an MR scanner. In summary, the needle can be set in motion
from a distance by either waving a magnet or by applying an alternating current to a coil. In
both situations, magnetic resonance is achieved when the magnetic field that motion or
alternating currents produce, oscillates at the resonance frequency. When the waving or the
alternating current is stopped, the radio waves that are subsequently produced by the
oscillating needle will induce a voltage over the coil.
MRI uses the magnetic properties of spinning hydrogen atoms to produce images. The first
step in MRI is the application of a strong, external magnetic field. For this purpose, the
patient is placed within a large powerful magnet. Most current medical MRI machines have
field strengths of 1.5 or 3.0 Tesla. The hydrogen atoms within the patient align in a direction
either parallel or antiparallel to the strong external field. A greater proportion aligns in the
parallel direction so that the net vector of their alignment, and therefore the net magnetic
vector, will be in the direction of the external field. This is known as longitudinal
magnetization. A second magnetic field is applied at right angles to the original external field.
This second magnetic field is known as the radiofrequency pulse (RF pulse), because it is
applied at a frequency in the same part of the electromagnetic spectrum as radio waves. A
magnetic coil, known as the RF coil, applies the RF pulse. The RF pulse causes the net
magnetization vector of the hydrogen atoms to turn towards the transverse plane, i.e. a plane
at right angles to the direction of the original, strong external field. The component of the net
magnetization vector in the transverse plane induces an electrical current in the RF coil. This
current is known as the MR signal and is the basis for formation of an image. Computer
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analysis of the complex MR signal from the RF receiver coils is used to produce an MR
image.
12.4.2. The magnetism of the body
Let‘s see how magnet needles with and without spin are affected by radio waves, we now
turn to the “compass needles” in our own bodies.
(a) Most frequently, the MR signal is derived from hydrogen nuclei (meaning the atomic nuclei
in the hydrogen atoms). Most of the body’s hydrogen is found in the water molecules. Few
other nuclei are used for MR.
(b) Hydrogen nuclei (also called protons) behave as small compass needles that align themselves
parallel to the field.
(c) The compass needles (the spins) are aligned in the field, but due to movements and nuclear
interactions in the soup, the alignment only happens partially.
(d) The nuclei in the body move among each other (thermal motion) and the net magnetization in
equilibrium is thus temperature dependent.
(e) Due to the number of hydrogen nuclei (about ) found in the body, the net magnetization
still becomes measurable. It is proportional to the field: A large field produces a high degree
of alignment and thus a large magnetization and better signal to noise ratio.
12.4.3. Magnetic Resonance Imaging (MRI).
In MRI, a particular type of nucleus is selected and its distribution in the body is monitored.
Hydrogen is the most commonly imaged element, not only due to its abundance in the body but also
because it gives the strongest MRI signals.
The technique uses a very powerful magnet to align the nuclei of atoms inside the body, and a
variable magnetic field that causes the atoms to resonate, a phenomenon called nuclear
magnetic resonance. The nuclei produce their own rotating magnetic fields that a scanner
detects and uses to create an image.
MRI is used to diagnose a variety of disorders, such as strokes, tumors, aneurysms, spinal
cord injuries, multiple sclerosis and eye or inner ear problems. It is also widely used in
research to measure brain structure and function, among other things.
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Fig: 12.16: showing a patient entering a MRI set up for exam.
An MRI scan can be used to examine almost any part of the body, including the:
brain and spinal cord
bones and joints
breasts
heart and blood vessels
internal organs, such as the liver, womb or prostate gland ,etc
The results of an MRI scan can be used to help diagnose conditions, plan treatments and
assess how effective previous treatment has been.
12.4.4. Functional of MRI Scan
Activity: 12.8
a) Explain the function of MRI Scan.
b) What are the advantages and disadvantages of MRI Scan?
c) What are the hazards associated with MRI?
There are many forms of MRI, some of them are:
a) Diffusion-weighted imaging.
Diffusion-weighted imaging (DWI) is sensitive to the random Brownian motion (diffusion) of
water molecules within tissue. The greater the amount of diffusion, the greater the signal loss
on DWI. Areas of reduced water molecule diffusion show on DWI as relatively high signal.
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Diffusion-weighted imaging is the most sensitive imaging test available for the diagnosis
of acute cerebral infarction. With the onset of acute ischaemia and cell death there is
increased intracellular water (cytotoxicoedema) with restricted diffusion of water molecules.
An acute infarct therefore shows on DWI as an area of relatively high signal.
b) Perfusion-weighted imaging
In perfusion-weighted imaging (PWI) the brain is rapidly scanned following injection of a
bolus of contrast material (gadolinium). The data obtained may be represented in a number of
ways including maps of regional cerebral blood volume, cerebral blood flow, and mean
transit time of the contrast bolus. PWI may be used in patients with cerebral infarct to map
out areas of brain at risk of ischaemia that may be salvageable with thrombolysis.
c) Magnetic resonance spectroscopy
Magnetic resonance spectroscopy (MRS) uses different frequencies to identify certain
molecules in a selected volume of tissue, known as a voxel. Following data analysis, a
spectrographic graph of certain metabolites is drawn. Metabolites of interest include lipid,
lactate, NAA (N-acetylaspartate), choline, creatinine, citrate and myoinositol. Uses of MRS
include characterization of metabolic brain disorders in children, imaging of dementias,
differentiation of recurrent cerebral tumour from radiation necrosis, and diagnosis of
prostatic carcinoma.
d) Blood oxygen level-dependent imaging
Blood oxygen level-dependent (BOLD) imaging is a non-invasive functional MRI (fMRI)
technique used for localizing regional brain signal intensity changes in response to task
performance. BOLD imaging depends on regional changes in concentration of
deoxyhemoglobin, and is therefore a tool to investigate regional cerebral physiology in
response to a variety of stimuli. BOLD fMRI may be used prior to surgery for brain tumor or
arteriovenous malformation (AVM), as a prognostic indicator of the degree of postsurgical
deficit.
12.4.5 Advantage and disadvantages of MRI.
Advantages of MRI in clinical practice include:
1. Excellent soft tissue contrast and characterization
2. Lack of ionizing radiation.
3. Noninvasive machine.
4. Lack of artefact from adjacent bones, e.g. pituitary fossa
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Disadvantages of MRI:
1. High capital and running costs.
2. Image selected and interpretation is complex.
3. Examination can be difficult for some people who are claustrophobic
4. The examination is noisy and takes long.
5. Hazards with implants, particularly pacemakers.
6. Practical problems associated with large superconducting magnets.
12.4.7. Checking my progress
1. What is meant by relaxation in the context of MRI?
2. Give the reasons why the hydrogen nucleus is most used in MRI.
3. What does NMR stand for? Explain carefully the role of the three terms involved
4. Draw the basic steps in the formation of MRI image.
12.5 ENDOSCOPY
ACTIVITY 12.9
a) How can we examine inside the stomach by using light rays?
b) How is endoscope performed?
12.3.1 Description
Endoscopy is a nonsurgical procedure used to examine a person's digestive tract. Using an
endoscope, which is a flexible tube with a light and camera attached to it, the specialist can
view pictures of your digestive tract on a monitor.
During an upper endoscopy, an endoscope is easily passed through the mouth and throat and
into the esophagus, allowing the specialist to view the esophagus, stomach, and upper part of
the small intestine.
Similarly, endoscopes can be passed into the large intestine (colon) through the rectum to
examine this area of the intestine.
12.3.2 Upper endoscopy
Upper Endoscopy (also known as gastroscopy, EGD, or esophagogastroduodenoscopy) is a
procedure that enables your surgeon to examine the lining of the esophagus (swallowing
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tube), stomach and duodenum (first portion of the small intestine). A bendable, lighted tube
about the thickness of your little finger is placed through your mouth and into the stomach
and duodenum.
Fig.12.17 Endoscopy exam
12.3.3. How is the upper endoscopy performed?
Upper endoscopy is performed to evaluate symptoms of persistent upper abdominal pain,
nausea, vomiting, difficulty swallowing or heartburn. It is an excellent method for finding the
cause of bleeding from the upper gastrointestinal tract. It can be used to evaluate the
esophagus or stomach after major surgery. It is more accurate than X-rays for detecting
inflammation, ulcers or tumors of the esophagus, stomach and duodenum. Upper endoscopy
can detect early cancer and can distinguish between cancerous and noncancerous conditions
by performing biopsies of suspicious areas.
Fig.12.18: Interior of a stomach
A variety of instruments can be passed through the endoscope that allows the surgeon to treat
many abnormalities with little or no discomfort, remove swallowed objects, or treat upper
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gastrointestinal bleeding. Safe and effective control of bleeding has reduced the need for
transfusions and surgery in many patients.
12.3.4. Advantages and disadvantages of endoscopy
Advantages
Complete visualization of the entire stomach or digestive tract.
It is very safe and effective tool in diagnosis
Does not leave any scar because it uses natural body openings.
It is cost effective and has low risk
They are generally painless.
Can do therapeutic interventions
Allows for sampling/biopsying of small bowel mucosa
Allows for resection of polyps.
Disadvantages:
Although the endoscope is very safe; however, the procedure has a few potential
complications which may include:
Bleeding
Perforation (tear in the gut wall)
Infection
Reaction to sedation (action of administering a sedative drug to produce a state of
calm or sleep.
Technically difficult procedure
Very time consuming (Procedure can take > 3 hours)
Patient may need to be admitted to the hospital
Higher risk of small bowel perforation
Case reports of pancreatitis and intestinal necrosis
Reported incidents of aspiration and pneumonia
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12.3.5 Checking my progress
1. What are instruments used to view the esophagus, stomach and upper small intestine of
human body?
2. Explain the function of endoscope.
3. Compare and contrast colonoscopy and gastroscopy
12.3.6. HAZARDS ASSOCIATED WITH MEDICAL IMAGING
The following are some hazards associated with medical imaging:
1. Exposure to ionizing radiation
2. Anaphylactoid reactions to iodinated contrast media
3. Contrast-induced nephropathy (CIN)
4. MRI safety issues
5. Nephrogenic systemic sclerosis (NSF) due to Gd-containing contrast media.
1. Exposure to ionizing radiation
Radiation effects and effective dose Radiography, scintigraphy and CT use ionizing radiation.
Numerous studies have shown that ionizing radiation in large doses is harmful. The risks of
harm from medical radiation are low, and are usually expressed as the increased risk of
developing cancer as a result of exposure. Radiation effects occur as a result of damage to
cells, including cell death and genetic damage. Actively dividing cells, such as are found in
the bone marrow, lymph glands and gonads are particularly sensitive to radiation effects.
2. Anaphylactoid contrast media reactions
Most patients injected intravenously with iodinated contrast media experience normal
transient phenomena, including a mild warm feeling plus an odd taste in the mouth. With
modern iodinated contrast media, vomiting at the time of injection is uncommon. More
significant adverse reactions to contrast media may be classified as mild, intermediate or
severe anaphylactoid reactions:
Mild anaphylactoid reactions: mild urticaria and pruritis
Intermediate reactions: more severe urticaria, hypotension and mild bronchospasm
Severe reactions: more severe bronchospasm, laryngeal oedema, pulmonary oedema,
unconsciousness, convulsions, pulmonary collapse and cardiac arrest.
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3. Contrast-induced nephropathy
Contrast-induced nephropathy (CIN) refers to a reduction of renal function (defined as
greater than 25 per cent increase in serum creatinine) occurring within 3 days of contrast
medium injection. Risk factors for the development of CIN include:
Pre-existing impaired renal function, particularly diabetic nephropathy, Dehydration, Sepsis,
Age>60 years, Recent organ transplant , Multiple myeloma.
The risk of developing CIN may be reduced by the following measures:
Risk factors should be identified by risk assessment questionnaire.
Use of other imaging modalities in patients at risk including US or non-contrast-
enhanced CT.
Use of minimum possible dose where contrast medium injection is required.
Adequate hydration before and after contrast medium injection.
Various pretreatments have been described, such as oral acetylcysteine; however,
there is currently no convincing evidence that anything other than hydration is
beneficial.
4. MRI safety issues
Potential hazards associated with MRI predominantly relate to the interaction of the magnetic
fields with metallic materials and electronic devices. Ferromagnetic materials within the
patient could possibly be moved by the magnetic field causing tissue damage. Common
potential problems include metal fragments in the eye and various medical devices such as
intracerebral aneurysm clips. Patients with a past history of penetrating eye injury are at risk
for having metal fragments in the eye and should be screened prior to entering the MRI room
with radiographs of the orbits. The presence of electrically active implants, such as cardiac
pacemakers, cochlear implants and neurostimulators, is generally a contraindication to MRI
unless the safety of an individual device is proven.
5. Nephrogenic systemic sclerosis
Nephrogenic systemic sclerosis (NSF) is a rare complication of some Gd-based contrast
media in patients with renal failure. Onset of symptoms may occur from one day to three
months following injection. Initial symptoms consist of pain, pruritis and erythema, usually in
the legs. As NSF progresses there is thickening of skin and subcutaneous tissues, and fibrosis
of internal organs including heart, liver and kidneys. Identifying patients at risk, including
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patients with known renal disease, diabetes, hypertension and recent organ transplant, may
reduce the risk of developing NSF following injection of Gd- based contrast media.
Risk reduction in MRI
A standard questionnaire to be completed by the patient prior to MRI should cover relevant
factors such as:
Previous surgical history
Presence of metal foreign bodies including aneurysm clips, etc.
Presence of cochlear implants and cardiac pacemakers
Possible occupational exposure to metal fragments and history of penetrating eye
injury
Previous allergic reaction to Gd-based contrast media
Known renal disease or other risk factors relevant to NSF.
END UNIT ASSESSMENT
Part I: Copy the following in your notebook and chose the correct answer
1.Which are included in the system components of gamma rays camera for producing image
of the body?
a. Collimator
b. Scintillation
c. Attenuation
d. All of the above
2. Which of the following modalities does not use a form of ionizing radiation?
a. Radiography.
b. Computed tomography.
c. Sonography.
d. Magnetic resonance imaging
3. Hazards not associated with modern medical imaging include:
a. Anaphylactoid reactions to iodinated contrast media
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b. Complication of some Gd-based contrast media in patients with renal failure.
c. Imaging of the breast improves a physician's ability to detect small tumors
d. Radiation effects and effective dose Radiography.
4. Medical imaging systems are often evaluated the characteristics which are directly related
to:
a. Image noise.
b. Image blurring.
c. Image unsharpness.
d. Visibility of anatomical detail.
5. Risks associated with radionuclide imaging are:
a. Generally poor resolution compared with other imaging modalities.
b. Rarely receiving an overdose of chemical injected in the vein of the body.
c. High capital and running costs
d. None of them.
Part II: Structured questions
6. Write the missing word or words on the space before each number.
A. The term ………………….. is often used to refer to X-ray CT.
B. Gastroscopy is a procedure that enables your surgeon to examine the lining of the
…………. C. The most sensitive imaging test available for the diagnosis of acute cerebral infarction
is …………...
D. Array of …………………. to transform the flashes into amplified electrical pulses
inside the body.
E. Transducers used are different depending on ………. of a patient, one has 5 MHz and
other 3.5 MHz.
F. Hydrogen nuclei (also called protons) behave as small …………… that align
themselves parallel to the field.
G. In ………………….. there are appearance three words: nuclear, magnetic and
resonance.
H. Examination can be ………………… is one of the disadvantages of MRI.
7. Answer by True if it is True and by False if it is False
a. The use of gamma radiation to form images following the injection of various
radiopharmaceuticals is known as Scintigraphy.
b. This decision to scan or not to scan a normal pregnancy must be made only by the
photographer. There are universally accepted guidelines at present.
c. Tissue in the body absorbs and scatters ultrasound in the same ways. Lower
frequencies are more rapidly absorbed (attenuated) than higher frequencies.
d. Upper endoscopy uses light and camera to view the esophagus, stomach, and upper
part of the small intestine.
e. Ultrasound is both generated and detected through high frequency oscillations in
piezoelectric crystals so there is ionizing radiation exposure associated with
ultrasound imaging.
8.Compare endoscopy imaging and radionuclide imaging
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9. What are the advantages of MRI in clinical practice?
10. Is ultrasound safe? explain.
11. What areas of the body can be imaged by ultrasound?
12. Why is ultrasound used in pregnancy?
13. Explain the advantage of CT scan
14. In mammography exams, is the breast compression necessary? Why
Essay question
Historically, MRI began in the central nervous system, but it is now extended to all regions of
the human body. The excellent resolution and contrast available in any chosen plane in the
body, makes the MRI an invaluable diagnostic tool with which to study body structure,
function and chemistry, as well as disease. Discuss the application of MRI.
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UNIT 13: RADIATIONS AND MEDICINE
Fig.13. 1 Various sources of radiation.
Key unit Competence
By the end of the unit the learner should be able to analyze the use of radiation in medicine.
My goals
Explain radiation dosimetry.
Differentiate the terms exposure, absorbed dose, quality factor (relative to biological
effectiveness) and dose equivalent as used in radiation dosimetry.
Differentiate physical half-life, biological half-life and effective half-life
Solve radiation dosimetry problems
Analyse the basics of radiation therapy for cancer.
Explain safety precautions when handling radiations
Describe the concept of balanced risk.
Introductory activity
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Radiation has always been present and is all around us. Life has evolved in a world containing
significant levels of ionizing radiation. Our bodies are adapted to it.
People are constantly exposed to small amounts of ionizing radiation from the environment as they
carry out their normal daily activities; this is known as background radiation. We are also exposed
through some medical treatments and through activities involving radioactive material.
Fig 13.1 above identifies four major sources of public exposure to natural radiation: cosmic
radiation, terrestrial radiation, inhalation and ingestion.
Brainstorm and try to answer the following questions:
a) Distinguish artificial source of radiation and natural source of radiation?
b) Explain briefly each major source of public exposure to natural radiation stated above.
c) Which kind of sources of radiation are mostly preferred to be used in medicine? Explain why
d) Does exposure to heavy ions at the level that would occur during deep-space missions of long
duration pose a risk to the integrity and function of the central nervous system? Explain to support
your idea.
13.1 RADIATION DOSE
13.1.1 Ionization and non-ionization radiations
Activity 13.1: Types of radiation
Radiation is the emission of particles or electromagnetic waves from a source. Radiation from
radioactive materials has the ability to interact with atoms and molecules of living objects.
a) With the help of the diagram below, distinguish the forms of radiation?
b) Which type do you think is mostly used in medical treatment? Explain your answer with
supporting arguments?
c) Suggest the possible side effects of using radiations in medicine? Which of the two forms of
radiation induces more side effects when exposed to human body? Explain to support your
choice.
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Fig.13. 2: Forms of radiation
In a neutral atom, the positive charge of the nucleus is equal and opposite to the total negative charge
of the orbital electrons. If such an atom loses or gains an electron, it becomes an ion. The atom will
now have a net positive or negative charge and is called an ion. This process is called ionization, and
the radiation responsible for it is called ionising radiation. When discussing the interaction of
radiations with matter in particularly in relation to health, two basic types of radiation can be
considered:
a. Ionizing radiation.
This is a radiation that carries enough energy to liberate electrons from atoms or molecules, thereby
ionizing them. As the more powerful form of radiation, ionizing radiation is more likely to damage
tissue than non-ionizing radiation. The main source of exposure to ionizing radiation is the radiation
used during medical exams such as X-ray radiography or computed tomography scans.
However, the amounts of radiation used are so small that the risk of any damaging effects is minimal.
Even when radiotherapy is used to treat cancer, the amount of ionizing radiation used is so carefully
controlled that the risk of problems associated with exposure is tiny.
All forms of living things emit a certain amount of radiation, with humans, plants and animals
accumulating radioisotopes as they ingest food, air and water. Some forms of radiation such as
potassium-40 emit high-energy rays that can be detected using measurement systems. Together with
the background radiation, these sources of internal radiation add to a person’s total radiation dose.
Background radiation is emitted from both naturally occurring and man-made sources. Natural
sources include cosmic radiation, radon radiation in the body, solar radiation and external terrestrial
radiation. Man-made forms of radiation are used in cancer treatment, nuclear facilities and
nuclear weapons.
Globally, the average exposure to ionizing radiation per year is around 3 milliSieverts (mSv), with
the main sources being natural (around 80%). The remaining exposure is due to man-made forms
such as those used in medical imaging techniques. Exposure to man-made forms of ionizing
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radiations is generally much higher in developed countries where the use of nuclear imaging
techniques is much more common than in developing countries.
b. Non-ionizing radiations
Non-ionizing radiation refers to any type of electromagnetic radiation that does not carry enough
energy to ionize atoms or molecules. Examples of non-ionizing radiations include visible light,
microwaves, ultraviolet (UV) radiation, infrared radiation, radio waves, radar waves, mobile phone
signals and wireless internet connections.
Although UV has been classified as a non-ionizing radiation but it has been proven that high levels
of UV-radiation can cause sunburn and increase the risk of skin cancer developing.
Scientific investigations suggest that the use of telecommunications devices such as mobile phones
may be damaging, but no risk associated with the use of these devices has yet been identified in any
scientific studies. This energy is emitted both inside the body and externally, through both natural
and man-made processes.
13.1.2 Radiation penetration in body tissue
Activity13.2:
The figure below shows the penetrating power of radiation represented by A, B and C. Use the figure
to answer the following questions.
Fig.13. 3 The penetrating power of radiation
Questions:
a) Interpret the figure and write the names of letters A, B and C labeled on the figure above?
b) Which of the three types of radiation has high penetrating power? Explain to support your idea.
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c) Outline four uses of the man-made sources of radiation?
d) How does radiation affect me? Explain clearly with scientific reasoning.
An important characteristic of the various ionising radiations is how deeply they can penetrate the
body tissues. X-rays, gamma rays, and neutrons of sufficient energy described below can reach all
tissues of the body from an external source.
Alpha Radiation
Alpha radiation occurs when an atom undergoes radioactive decay, giving off an α- particle
consisting of two protons and two neutrons (essentially the nucleus of a helium-4 atom) following
the equation
𝑋 → 𝑌 +𝑍−2𝐴−4
𝑍𝐴 𝐻𝑒2
4
Due to their charge and mass, alpha particles interact strongly with matter, and can only travel a few
centimeters in air. A thin sheet of paper, on the other hand, stops alpha particles. They are also
stopped by the superficial dead layer of skin that is only 70 µm thick. Therefore, radionuclides that
emit only alpha particles are harmless unless you take them into the body. This you might do by
inhalation (breathing in) or ingestion (eating and drinking).
Beta Radiation
Beta radiation takes the form of either an electron or a positron (a particle with the size and mass of
an electron, but with a positive charge) being emitted from an atom.
Due to their smaller mass, they are able to travel further in air, up to a few meters, and can be
stopped by a thick piece of plastic, or even a stack of paper. Such radiation can penetrate the skin a
few centimeters, posing somewhat of an external health risk. The depth to which beta particles can
penetrate the body depends on their energy.
High-energy beta particles (several MeV) may penetrate a cm of a tissue, although most are absorbed
in the first few mm. As a result, beta emitters outside the body are hazardous only to surface tissues
such as the skin or the lenses of the eye. When you take beta emitters into the body, they will
irradiate internal tissues and then become a much more serious hazard.
Gamma Radiation
Gamma radiation, unlike alpha or beta, does not consist of any particles, instead consisting of a
photon of energy being emitted from an unstable nucleus. Having no mass or charge, gamma
radiation can travel much farther through air than alpha or beta, losing (on average) half its energy.
Gamma waves can be stopped by a thick or dense enough layer material, with high atomic number.
Materials such as lead can be used as the most effective form of shielding.
X-Rays
X-rays are similar to gamma radiation, with the primary difference being that they originate from the
electron cloud. This is generally caused by energy changes in an electron, such as moving from a
higher energy level to a lower one, causing the excess energy to be released. X-Rays are longer-
wavelength and (usually) lower energy than gamma radiation, as well.
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Neutron Radiation
Neutron radiation consists of a free neutron, usually emitted as a result of spontaneous or induced
nuclear fission. They are able to travel hundreds or even thousands of meters in air, they are however
able to be effectively stopped if blocked by a hydrogen material, such as concrete or water.
Neutron radiation occurs when neutrons are ejected from the nucleus by nuclear fission and other
processes. The nuclear chain reaction is an example of nuclear fission, where a neutron being ejected
from one fission atom will cause another atom to fission, ejecting more neutrons. Unlike other
radiations, neutron radiation is absorbed by materials with lots of hydrogen atoms, like paraffin wax
and plastics.
Fig.13. 4: Types of ionizing radiation
13.1.3 Radiation dosimetry
Activity13.3:
a) What does the term Dosimeter in radiation dosimetry mean?
b) Who Should Wear a Dosimeter? Suggest reasons why it is very important to wear a dosimeter?
Just as for drugs, the effect of radiation depends on the amount a person has received. Therefore,
amounts of radiation received are referred to as doses, and the measurement of such doses is known
as dosimetry.
Dosimeters are used to monitor your occupational dose from radioactive material or radiation-
producing equipments. Most individuals working with X-ray producing equipment in the hospital
will be issued with a dosimeter. For those individuals working in the research laboratory setting,
dosimeters will be issued based on the nuclide and total activity that will be used.
Dosimeters are integrating detectors; that is, they accumulate the radiation dose and give off an
amount of light which is proportional to that dose.
The energy absorption properties of dosimeters are designed to be very similar to tissue, so they are
very effective as personnel dosimeters. These devices are used to measure exposures from x-ray,
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gamma ray and high energy beta particles. Dosimeters are not suitable for measuring exposures to
low energy beta particles or alpha particles.
13.1.4 Radiation exposure
Activity13.4:
a) What are the symptoms of radiation exposure?
b) Explain briefly the effects of radiation exposure to the human body?
c) It is possible that side effects can happen when a person undergoes radiation treatment for cancer.
Suggest the common side effects of radiation exposure to the human body?
d) Does radiation exposure to the human body induce risks? Support your decision with clear
explanations.
Long-term exposure to small amounts of radiation can lead to gene mutations and increase the risk
of cancer, while exposure to a large amount over a brief period can lead to radiation sickness.
Exposure is a measure of the ionization produced in air by X-rays or rays, and it is defined in the
following manner. A beam of X-rays or rays is sent through a mass m of dry air at standard
temperature and pressure ( stp: C00 , 1 atm). In passing through the air, the beam produces positive
ions whose total charge is q. Exposure is defined the total charge per unit mass of air. The SI unit
for exposure is coulomb per unit mass ( kgC / ).
The commonly used unit for exposure E is the roentgen (R). 1R is the amount of electromagnetic
radiation which produces in one gram of air 2.58𝑥10−7C at normal temperature (22℃) and pressure
(760mmHg) conditions. kgCR /1058.21 4
Since the concept of exposure is defined in terms of the ionizing abilities of X-rays and rays in
air, it does not specify the effect of radiation on living tissue. For biological purposes, the absorbed
dose is more suitable quantity, because it is the energy absorbed from the radiation per unit mass of
absorbing material.
13.1.5 Absorbed radiation dose
Activity13.5
a) What does the term absorbed dose mean in medical treatment?
b) In the application of radiation in medicine, we use the statement “A measure of the risk of
biological harm”. Brainstorm and explain clearly what the statement means.
c) Explain why doses of alpha and gamma radiation produce unequal biological effects?
What is important when we analyze the effect of radiation on human being is not so much the total
dose to the whole system but the dose per kg. That's why a doctor will prescribe smaller doses of
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medicine for children than for adults. A similar approach is used in radiation protection
measurements, where the unit of absorbed dose is specified in terms of the amount of energy
deposited by radiation in 1 kg of material. This unit is the Gray, abbreviated Gy. It was named in
honor of Louis Gray, who was a very big name in the early days of radiation dosimetry. An absorbed
radiation dose of 1 Gray corresponds to the deposition of 1 joule of energy in 1 kg of material. The
gray is a measure of energy absorbed by 1 kg of any material, be it air, water, tissue or whatever. A
person who has absorbed a whole body dose of 1 Gy has absorbed one joule of energy in each kg of
its body tissue.
As we shall see later, the gray is a fairly hefty dose, so for normal practical purposes we use the
milligray (abbreviated mGy) and the microgray (abbreviated µGy).
The gray is a physical unit. It describes the physical effect of the incident radiation (i.e., the amount
of energy deposited per kg), but it tells us nothing about the biological consequences of such energy
deposition in tissue. Studies have shown that alpha and neutron radiation cause greater biological
damage for a given energy deposition per kg of tissue than gamma radiation does.
In other words, equal doses of, say, alpha and gamma radiation produce unequal biological effects.
This is because the body can more easily repair damage from radiation that is spread over a large
area than that which is concentrated in a small area. Because more biological damage is caused for
the same physical dose.
13.1.6 Quality factors
Quality factors are used to compare the biological effects from different types of radiation. For
example, fast neutron radiation is considered to be 20 times as damaging as X-rays or gamma
radiation. You can also think of fast neutron radiation as being of "higher quality", since you need
less absorbed dose to produce equivalent biological effects. This quality is expressed in terms of the
Quality Factor (Q). The quality factor of a radiation type is defined as the ratio of the biological
damage produced by the absorption of 1 Gy of that radiation to the biological damage produced by 1
Gy of X or gamma radiation.
The Q of a certain type of radiation is related to the density of the ion tracks it leaves behind it in
tissue; the closer together the ion pairs, the higher the Q.
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13.1.7 Equivalent dose
The absorbed radiation dose, when multiplied by the Q of the radiation delivering the dose, will give
us a measure of the biological effect of the dose. This is known as the equivalent dose. The unit of
equivalent dose H is the Sievert (Sv). An equivalent dose of one Sievert represents that quantity of
radiation dose that is equivalent, in terms of specified biological damage, to one gray of X or gamma
rays.
In practice, we use the millisievert (mSv) and microsievert (µSv). The sievert is the unit that we use
all the time, because it is the only one that is meaningful in terms of biological harm. In calculating
the equivalent dose from several types of radiation (we call this "mixed radiation"), all measurements
are converted to Sv, mSv or µSv and added.
Most of the radiation instruments we use to measure doses or dose rates read in mSv or µSv. Few
other instruments can read in mGy or µGy, but they measure only gamma radiation.
The table 13.1 lists some typical relative biological effectiveness ( BER ) values for different kinds of
radiation, assuming that an average biological tissue is being irradiated. The values of 1BER
indicate that rays and 𝛽− particles produce the same biological damage as do 200 keV X-rays. The
large BER values indicate that protons, -particles, and fast neutrons cause substantially more
damage.
Types of radiation BER Types of radiation
BER
200 keV X-rays 1 particles 1
rays 1 particles 10-20
Protons 10 Neutrons
Slow 2 Fast 10
Table 13. 1: Relative biological effectiveness for various types of radiation
13.1.8 Radiation protection
The effects of radiation at high doses and dose rates are reasonably well documented. A very large
dose delivered to the whole body over a short time will result in the death of the exposed person
within days.
We know from these that some of the health effects of exposure to radiation do not appear unless a
certain quite large dose is absorbed. However, many other effects, especially cancers are readily
detectable and occur more often in those with moderate doses. At lower doses and dose rates, there is
a degree of recovery in cells and in tissues.
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Radiation protection sets examples for other safety disciplines in two unique respects:
First, there is the assumption that any increased level of radiation above natural background will
carry some risk of harm to health.
Second, it aims to protect future generations from activities conducted today.
The use of radiation and nuclear techniques in medicine, industry, agriculture, energy and other
scientific and technological fields has brought tremendous benefits to society. The benefits in
medicine for diagnosis and treatment in terms of human lives saved are large in size..
No human activity or practice is totally devoid of associated risks. Radiation should be viewed from
the perspective that the benefit from it to mankind is less harmful than from many other agents.
Quick check 13.2: At what level is radiation harmful? Explain your idea
Note: The optimization of patients' protection is based on a principle that the dose to the irradiated
target (tumor) must be as high as it is necessary for effective treatment while protecting the healthy
tissues to the maximum extent possible.
13.1.9 Checking my progress
1. Does receiving external-beam radiation make a person radioactive or able to expose others to
radiation? Explain to support idea
2. How can I be sure that the external-beam radiating machine isn’t damaging normal, healthy tissue
in my body? Explain clearly with scientific reasoning.
3. I am having an imaging test using radioactive materials. Will I be radioactive after the test?
Comment to support your decision.
4. All my radioactive material is secured properly and I have empty waste containers in the lab. Do I
have to lock the room? Explain clearly to justify your decision.
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13.2 BIOLOGICAL EFFECTS OF RADIATION EXPOSURE
13.2.1 Deterministic and stochastic effects:
Activity 13. 6:
1. Is the use of ionizing radiation in medicine beneficial to human health? Explain to support your
point.
2. Are there risks to the use of ionizing radiation in medicine? Explain your answer.
3. How do we quantify the amount of radiation?
4. What do we know about the nature (mechanism) of radiation-induced biological effects?
5. How are effects of radiation classified?
Effects of radiations due to cell killing have a practical threshold dose below which the effect is not
evident but in general when the effect is present its severity increases with the radiation dose.
The threshold doses are not an absolute number and vary somewhat by individual. Effects due to
mutations (such as cancer) have a probability of occurrence that increases with dose.
a. Deterministic effects:
These effects are observed after large absorbed doses of radiation and are mainly a consequence of
radiation induced cellular death. They occur only if a large proportion of cells in an irradiated tissue
have been killed by radiation, and the loss can be compensated by increasing cellular proliferation.
b. Stochastic effects:
They are associated with long term, low level (chronic) exposure to radiation. They have no
apparent threshold. The risk from exposure increases with increasing dose, but the severity of the
effect is independent of the dose.
Irradiated and surviving cells may become modified by induced mutations (somatic, hereditary).
These modifications may lead to two clinically significant effects: malignant neoplasm (cancer) and
hereditary mutations.
The frequency or intensity of biological effects is dependent upon the total energy of radiation
absorbed (in joules) per unit mass (in kg) of a sensitive tissues or organs. This quantity is called
absorbed dose and is expressed in gray (Gy).
In evaluating biological effects of radiation after partial exposure of the body further factors such as
the varying sensitivity of different tissues and absorbed doses to different organs have to be taken
into consideration.
To compare risks of partial and whole body irradiation at doses experienced in diagnostic radiology
and nuclear medicine a quantity called equivalent or effective dose is used. A cancer caused by a
small amount of radiation can be just as malignant as one caused by a high dose.
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Activity 13.7:
1. What is magnitude of the risk for cancer and hereditary effects?
2. Is ionizing radiation from medical sources the only one to which people is exposed?
3. What are typical doses from medical diagnostic procedures?
4. Can radiation doses in diagnosis be managed without affecting the diagnostic benefit? Explain to
support your decision.
5. Are there situations when diagnostic radiological investigations should be avoided? Explain to
support your decision.
The lifetime value for the average person is roughly a 5% increase in fatal cancer after a whole body
dose of 1 Sv. It appears that the risk in fetal life, in children and adolescents exceeds somewhat this
average level (by a factor of 2 or 3) and in persons above the age of 60 it should be lower roughly by
a factor of ~ 5.
Animal models and knowledge of human genetics, the risk of hereditary deleterious effects have
been estimated to not be greater than 10% of the radiation induced carcinogenic risk.
All living organisms on this planet, including humans, are exposed to radiation from natural sources.
An average yearly effective dose from natural background amounts to about 2.5 mSv. This exposure
varies substantially geographically (from 1.5 to several tens of mSv in limited geographical areas).
Various diagnostic radiology and nuclear medicine procedures cover a wide dose range based upon
the procedure. Doses can be expressed either as absorbed dose to a single tissue or as effective dose
to the entire body which facilitates comparison of doses to other radiation sources (such as natural
background radiation.
There are several ways to reduce the risks to very, very low levels while obtaining very beneficial
health effects of radiological procedures.
Quality assurance and quality control in diagnostic radiology and nuclear medicine play also a
fundamental role in the provision of appropriate, sound radiological protection of the patient.
There are several ways that will minimize the risk without sacrificing the valuable information that
can be obtained for patients' benefit. Among the possible measures it is necessary to justify the
examination before referring a patient to the radiologist or nuclear medicine physician.
Failure to provide adequate clinical information at referral may result in a wrong procedure or
technique being chosen by radiologist or nuclear medicine specialist.
An investigation may be seen as a useful one if its outcome - positive or negative - influences
management of the patient. Another factor, which potentially adds to usefulness of the investigation,
is strengthening confidence in the diagnosis. Irradiation for legal reasons and for purposes of
insurance should be carefully limited or excluded.
Activity 13.8:
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1. Are there special diagnostic procedures that should have special justification? Explain to support
your decision.
2. Do children and pregnant women require special consideration in diagnostic procedures?
3. What can be done to reduce radiation risk during the performance of a diagnostic procedure?
While all medical uses of radiation should be justified, it stands to reason that the higher the dose and
risk of a procedure, the more the medical practitioner should consider whether there is a greater
benefit to be obtained.
Among these special position is occupied by computed tomography (CT), and particularly its most
advanced variants like spiral or multi slice CT.
Both the fetus and children are thought to be more radiosensitive than adults. Diagnostic radiology
and diagnostic nuclear medicine procedures (even in combination) are extremely unlikely to result in
doses that cause malformations or a decrease in intellectual function. The main issue following in
childhood exposure at typical diagnostic levels (<50 mGy) is cancer induction.
Medically indicated diagnostic studies remote from the fetus (e.g. radiographs of the chest or
extremities, ventilation/perfusion lung scan) can be safely done at any time of pregnancy if the
equipment is in proper working order. Commonly the risk of not making the diagnosis is greater than
the radiation risk.
If an examination is typically at the high end of the diagnostic dose range and the fetus is in or near
the radiation beam or source, care should be taken to minimize the dose to the fetus while still
making the diagnosis. This can be done by tailoring the examination and examining each radiograph
as it is taken until the diagnosis is achieved and then terminating the procedure
For children, dose reduction in achieved by using technical factors specific for children and not using
routine adult factors. In diagnostic radiology care should be taken to minimize the radiation beam to
only the area of interest. Because children are small, in nuclear medicine the use of administered
activity lower than that used for an adult will still result in acceptable images and reduced dose to the
child.
The most powerful tool for minimizing the risk is appropriate performance of the test and
optimization of radiological protection of the patient. These are the responsibility of the radiologist
or nuclear medicine physician and medical physicist.
The basic principle of patients' protection in radiological X-ray investigations and nuclear medicine
diagnostics is that necessary diagnostic information of clinically satisfactory quality should be
obtained at the expense of a dose as low as reasonably achievable, taking into account social and
financial factors.
13.2.2 Effects of radiation exposure
Quick check13.1: Will small radiation doses hurt me?
Some effects may occur immediately (days or months) while others might take tens of years or even
get passed to the next generation. Effects of interest for the person being exposed to radiation are
called somatic effects and effects of interest that affect our children are called genetic effects.
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i. Radiation Health Effects
Ionizing radiation has sufficient energy to cause chemical changes in cells and damage them. Some
cells may die or become abnormal, either temporarily or permanently. By damaging the genetic
material (DNA) contained in the body’s cells, radiation can cause cancer.
Fortunately, our bodies are extremely efficient at repairing cell damage. The extent of the damage to
the cells depends upon the amount and duration of the exposure, as well as the organs exposed.
Exposure to an amount of radiation all at once or from multiple exposures in a short period of time.
In most cases, a large acute exposure to radiation causes both immediate ( radiation sickness) and
delayed effects (cancer or death), can cause sickness or even death within hours or days. Such acute
exposures are extremely rare.
ii. Chronic Exposure
With chronic exposure, there is a delay between the exposure and the observed health effect. These
effects can include cancer and other health outcomes such as benign tumors, cataracts, and
potentially harmful genetic changes.
Some radiation effects may occur immediately (days or months) while others might take years or
even get passed to the next generation. Effects of interest for the person being exposed to radiation
are called somatic effects and effects of interest that affect our children are called genetic effects.
a) Low levels of radiation exposure
Activity13.5:
a) What is the safe level of radiation exposure? Explain your answer.
b) What is the annual radiation exposure limit? Explain your answer
Radiation risks refer to all excess cancers caused by radiation exposure (incidence risk) or only
excess fatal cancers (mortality risk). Risk may be expressed as a percent, a fraction, or a decimal
value.
For example, a 1% excess risk of cancer incidence is the same as a 1 in a hundred (1/100) risk or a
risk of 0.01. However, it is very hard to tell whether a particular cancer was caused by very low
doses of radiation or by something else.
While experts disagree over the exact definition and effects of “low dose”. Radiation protection
standards are based on the premise that any radiation dose carries some risk, and that risk increases
directly with dose.
Note:
The risk of cancer from radiation also depends on age, sex, and factors such as tobacco use.
Doubling the dose doubles the risk.
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Acute health effects occur when large parts of the body are exposed to a large amount of radiation.
The large exposure can occur all at once or from multiple exposures in a short period of time.
Instances of acute effects from environmental sources are very rare.
13.2.3 Safety precautions for handling radiations
Activity 13.10: Safety precautions to be recognized when handling radiations
a) Who is involved in planning my radiation treatment?
b) How is the treatment plan checked to make sure it is best for me?
c) What procedures do I have in place so that the treatment team is able to treat me safely?
d) How can I be assured that my treatment is being done correctly every day?
e) What is the difference between a medical error and a side effect?
f) Outline the measures taken to reduce doses from external exposure
Shortening the time of exposure, increasing distance from a radiation source and shielding are the
basic countermeasures (or protective measures) to reduce doses from external exposure.
Fig.13. 5 Illustration of distance and time from source of radiation
Note: Time: The less time that people are exposed to a radiation source, the less the absorbed dose Distance: The
farther away that people are from a radiation source, the less the absorbed dose.
Fig.13. 6 Illustration of shielding
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Note: Shielding: Barriers of lead, concrete or water can stop radiation or reduce radiation intensity.
There are four main factors that contribute to how much radiation a person absorbs from a source.
The following factors can be controlled to minimize exposure to radiation:
i. The distance from the source of radiation
The intensity of radiation falls sharply with greater distance, as per the inverse square law. Increasing
the distance of an individual from the source of radiation can therefore reduce the dose of radiation
they are exposed to.
For example, such distance increases can be achieved simply by using forceps to make contact with
a radioactive source, rather than the fingers.
ii. Duration of exposure
The time spent exposed to radiation should be limited as much as possible. The longer an individual
is subjected to radiation, the larger the dose from the source will be.
One example of how the time exposed to radiation and therefore radiation dose may be reduced is
through improving training so that any operators who need to handle a radioactive source only do so
for the minimum possible time.
iii. Reducing incorporation into the human body
Potassium iodide can be given orally immediately after exposure to radiation. This helps protect the
thyroid from the effects of ingesting radioactive iodine if an accident occurs at a nuclear power plant.
Taking Potassium iodide in such an event can reduce the risk of thyroid cancer developing.
iv. Shielding
Shielding refers to the use of absorbent material to cover the source of radiation, so that less
radiation is emitted in the environment where humans may be exposed to it. These biological shields
vary in effectiveness, depending on the material’s cross-section for scattering and absorption.
The thickness (shielding strength) of the material is measured in g/cm2. Any amount of radiation that
does penetrate the material falls exponentially with increasing thickness of the shield.
Some examples of the steps taken to minimize the effects of radiation exposure are described below;
- The exposed individual is removed from the source of radiation.
- If radiation exposure has led to destruction of the bone marrow, the number of healthy white
blood cells produced in the bone marrow will be depleted.
- If only part of the body has been exposed to radiation rather than the whole body, treatment may
be easier because humans can withstand radiation exposure in large amounts to non-vital body
parts.
In every medicine there is a little poison. If we use radiation safely, there are benefits and if we use
radiation carelessly and high doses result, there are consequences.
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Ionizing radiation can change the structure of the cells, sometimes creating potentially harmful
effects that are more likely to cause changes in tissue. These changes can interfere with cellular
processes so cells might not be able to divide or they might divide too much.
Radioactive rays are penetrating and emit ionizing radiation in the form of electromagnetic waves
or energetic particles and can therefore destroy living cells. Small doses of radiation over an
extended period may cause cancer and eventually death. Strong doses can kill instantly. Marie Curie
and Enrico Fermi died due to exposure to radiation.
Several precautions should be observed while handling radioisotopes. Some of these are listed in the
following:
No radioactive substance should be handled with bare hands. Alpha and beta emitters can be
handled using thick gloves. Gamma ray emitters must be handled only by remote control that is
by mechanical means. Gamma rays are the most dangerous and over exposure can lead to serious
biological damage.
Radioactive materials must be stored in thick lead containers.
Reactor and laboratories dealing with and conducting experiments with radioactive metals must
be surrounded with thick concrete lined with lead.
People working with radioactive isotopes must wear protective clothing which is left in the
laboratory. The workers must be checked regularly with dosimeters, and appropriate measures
should be taken in cases of overdose.
Radioactive waste must be sealed and buried deep in the ground.
13.2.3 Checking my progress
1a) what does the term background radiation mean?
b) Hat is radiation – am I exposed to background radiation each day even if I do not have an X-ray
examination?
2. What are the risks associated with radiation from diagnostic X-ray imaging and nuclear medicine
procedures?
3. How do I decide whether the risks are outweighed by the benefits of exposure to X-radiation when
I have a radiology test or procedure?
4. Are there alternatives to procedures that involve ionizing radiation that would answer my doctor’s
question? Justify your answer with clear facts.
5. What kinds of safety checks do you perform each day?
6. How often does the medical physicist check the various machines involved during my treatment
are working properly?
7. If I have side effects after my treatment, who can I call?
a. My best friend
b. My primary care doctor
8. I have a question about a radiation treatment I had many years ago. Who should I call?
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13.3 CONCEPT OF BALANCED RISK.
13.3.1 Risks of ionizing radiation in medical treatment
Activity13.12: balanced risk
Brainstorm and write briefly how balance risks in medical treatment occur?
Risk in the area of radiation medicine has several dimensions that are less common in other areas of
medicine. First, there may be risks from overexposure that do not cause immediate injury. For
example, the causal connection, if any, may be difficult or impossible to verify for a malignancy that
surfaces several years after an inappropriate exposure.
Second, the risks associated with the medical use of ionizing radiation extend beyond the patient and
can affect health care workers and the public.
In amplifying these and other aspects of the risks that attend medical uses of ionizing radiation, the
discussion addresses the following issues: human error and unintended events; rates of
misadministration in radiation medicine; inappropriate and unnecessary care; and efforts that reduce
misadministration and inappropriate care.
13.3.2 Human Error and Unintended Events
Errors occur throughout health care: A pharmacist fills a prescription with the wrong medicine; an x-
ray technician takes a film of the wrong leg; a surgeon replaces the wrong hip. The advent of
complex medical technology has increased the opportunity for error even as it has increased the
opportunity for effecting cures.
By educating health care workers, and by circumscribing their actions, human error may be
minimized. However, some number of mistakes will always, unavoidably, be made, and no amount
of training or double-checking can erase that fact.
13.3.3 Comparison of risks in the use of ionizing radiation
The comparison of relative risks of misadministration in by-product radiation medicine to error rates
and events in other medical practice settings, as well as the comparison of disease and death rates
with the risks of the therapeutic administration itself, help to some extent to place ionizing radiation
use in a broader context.
To achieve this success requires the highest standards of performance (accuracy of delivered dose),
both when planning irradiation for an individual patient and in actual delivery of the dose.
In a large number of cases, decreasing the dose to the target volume is not possible since it would
unacceptably decrease the cure rate. In these cases present technological developments aim at
optimizing the patients’ protection, keeping the absorbed tumor dose as high as is necessary for
effective treatment while protecting nearby healthy tissues.
It should be remembered that successful eradication of a malignant tumor by radiation therapy
requires high-absorbed doses and there is a delayed (and usually low) risk of late complication. The
above mention techniques are used to provide the best benefit/risk ratio.
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A malignant tumor in a pregnant woman may require radiotherapy in attempt to save life of the
patient. If a tumor is located in a distant part of the body, the therapy - with individually tailored
protection of the abdomen (screening) - may proceed.
When thyroid cancer with metastases is diagnosed in a pregnant woman, treatment with 131I is not
compatible with continuation of the pregnancy. The treatment should then be delayed until delivery
if doing so wouldn’t put the mother’s life in danger.
Medical radiation can be delivered to the patient from a radiation source outside the patient.
Regardless of how much dose the patient received, they do not become radioactive or emit radiation.
. Balancing risks are often summarized in the following:
The demand for imaging, especially computed tomography, that has increased vastly over the
past 20 years
An estimated 30% of computed tomography tests that may be unnecessary
Ionizing radiation that may be associated with cancer.
The risks of radiation exposure that is often overlooked and patients are seldom made aware
of these risks
The requesting doctor who must balance the risks and benefits of any high radiation dose
imaging test, adhering to guideline recommendations if possible
Difficult cases that should be discussed with a radiologist, ideally at a clinic radiological or
multidisciplinary team meeting.
13.3.4 Checking my progress
1. When patients are intentionally exposed to ionizing radiation for medical purposes, do they
suffer unintentional exposures as a result of error or accident? Comment to support your idea.
2. What can be done to reduce radiation risk during conduct of radiation therapy?
3. Can pregnant women receive radiotherapy? Explain to support your decision.
4. Can patients’ treatment with radiation affect other people? Explain to support your decision.
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13.4 THE HALF-LIVES: PHYSICAL, BIOLOGICAL, AND EFFECTIVE
Activity 13.14: Distinguish between physical half-life, biological half-life and effective half-life
Brainstorm and write the distinction between physical half-life, biological half-life and effective half-
life in your note books.
The half-life is a characteristic property of each radioactive species and is independent of its amount
or condition. The effective half-life of a given isotope is the time in which the quantity in the body
will decrease to half as a result of both radioactive decay and biological elimination.
There are three half-lives that are important when considering the use of radioactive drugs for both
diagnostic and therapeutic purposes. While both the physical and biological half-lives are important
since they relate directly to the disappearance of radioactivity from the body by two separate
pathways (radioactive decay, biological clearance), there is no half-life as important in humans as the
effective half-life.
The half-life takes into account not only elimination from the body but also radioactive decay. If
there is ever a question about residual activity in the body, the calculation uses the effective half-life;
in radiation dosimetry calculations, the only half-life that is included in the equation is the effective
half-life.
13.4.1 Physical half Lives
Physical half-life is defined as the period of time required to reduce the radioactivity level of a
source to exactly one half its original value due solely to radioactive decay. The physical half-life is
designated pT or more commonly T1/2.
By default, the term T1/2 refers to the physical half-life and pT is used when either or both of the
other two half-lives are included in the discussion.
𝑇1
2
=𝑙𝑛2
𝜆,
where λ is the radioactive constant of the radio substance
There are a few things to note about the pT :
• The pT can be measured directly by counting a sample at 2 different points in time and then
calculating what the half-life is.
• For example, if activity decreases from 100% to 25% in 24 hours, then the half-life is 12 hours
since a decrease from 100% to 50% to 25% implies that 2 half-lives have elapsed.
The physical half-life is unaffected by anything that humans can do to the isotope. High or low
pressure or high or low temperature has no effect on the decay rate of a radioisotope.
14.4.2 Biological half lives
Biological Half-life is defined as the period of time required to reduce the amount of a drug in an
organ or the body to exactly one half its original value due solely to biological elimination. It is
typically designated bT . There are a few things to note about the bT :
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For radioactive compounds, we have to calculate the bT because the mass of the isotope is
usually on the nanogram scale and, when distributed throughout the body, and especially in
the target organ, concentrations are in the pictogram/ml range, much too small to measure
directly.
For non-radioactive compounds, we can measure the bT directly. For example, assuming that
a person is not allergic to penicillin, we could give 1 000 mg of the drug and then measure the
amount present in the blood pool and in the urine since we administered such a large amount
of the drug.
bT is affected by many external factors. Perhaps the two most important are hepatic and renal
function. If kidneys are not working well, we would expect to see a high background activity
on our scans.
Each individual organ in the body has its own bT and the whole body also has a bT
representing the weighted average of the bT of all internal organs and the blood pool. It is
therefore very important to have a frame of reference. For example, do you need to know the
bT of the drug in the liver or in the whole body?
All drugs have a bT , not just radioactive ones. Drug package inserts often refer to the half-
time of clearance of a drug from the blood pool or through the kidneys.
Since the whole body has a bT representing the weighted average of the bT of all internal
organs, it will almost never equal that of an internal organ.
13.4.3 Effective half lives
Effective half-life is defined as the period of time required to reduce the radioactivity level of an
internal organ or of the whole body to exactly one half its original value due to both elimination and
decay.
It is designated eT can be measured directly. For example, one can hold a detection device 1 m from
the patient’s chest and count the patient multiple times until the reading decreases to half of the
initial reading.
The patient is permitted to use the rest room between readings as needed, so both elimination and
decay are taking place. The half-life being measured in this case is the eT and eT is affected by the
same external factors that affect bT since eT is dependent upon bT .
bp
bp
eTT
TTT
Where
- T p: physical half-life
- bT : biological half-life
- Example 13.1
For a Xe-133 for pulmonary ventilation study, where pT = 5.3 days and bT = 15 s, calculate the
effective half-life of Xe.
Answer
We convert first Tp in seconds i.e. Tp=457920 s
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. sTT
TTT
bp
bp
e 1515457920
15457920
13.4.4 Checking my progress
1. I-131 sodium iodide has a bT of 24 days. What is eT if dTp 8 ?
2. A Tc-99 m compound has a eT = 1 days. What is bT if dTp 6
3. A radiopharmaceutical has a biological half-life of 4.00 hr and an effective half-life of 3.075 hr.
What isotope was used?
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13.5 END UNIT ASSESSMENT
13.5.1 Multiple choice
1. Which of the following would reduce the cell damage due to radiation for a lab technician who
works with radioactive isotopes in a hospital or lab?
A. Increase the worker’s distance from the radiation source.
B. Decrease the time the worker is exposed to the radiation.
C. Use shielding to reduce the amount of radiation that strikes the worker.
D. Have the worker wear a radiation badge when working with the radioactive isotopes.
E. All of the above.
2. If the same dose of each type of radiation was provided over the same amount of time, which type
would be most harmful?
A. X-rays. C. rays.
B. Rays. D. particles.
3. Which of the following is true?
A. Any amount of radiation is harmful to living tissue.
B. Radiation is a natural part of the environment.
C. All forms of radiation will penetrate deep into living tissue.
D. None of the above is true.
4. Which radiation induces the most biological damage for a given amount of energy deposited in
tissue?
A. Alpha particules. C. Beta radiation.
B. Gamma radiation. D. All do the same damage for the same deposited energy.
5. Which would produce the most energy in a single reaction?
A. The fission reaction associated with uranium-235.
B. The fusion reaction of the Sun (two hydrogen nuclei fused to one helium nucleus).
C. Both (A) and (B) are about the same.
D. Need more information.
6. The fuel necessary for fusion-produced energy could be derived from
A. water. D. superconductors.
B. uranium. E. helium.
C. sunlight.
13.5.2 Structured questions
7. If the equipment isn't working and my treatment is delayed or postponed, who checks that it is
safe to use again? And will this delay affect my cancer?
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8. Do you have weekly chart rounds where you review patient-related information in peer review?
9. Will you take imaging scans regularly during my treatment to verify position of my treatment?
Who reviews those scans?
10. People who work around metals that emit alpha particles are trained that there is little danger
from proximity or touching the material, but they must take extreme precautions against ingesting it.
Why? (Eating and drinking while working are forbidden.)
11. What is the difference between absorbed dose and effective dose? What are the SI units for each?
12. Radiation is sometimes used to sterilize medical supplies and even food. Explain how it works.
13. How might radioactive tracers be used to find a leak in a pipe?
14. Explain that there are situations in which we may or may not have control over our exposure to
ionizing radiation.
a) When do we not have control over our exposure to radiation?
b) When do we have control over our exposure to radiation?
c) Why might we want to limit our exposure to radiation when possible?
15. Does exposure to heavy ions at the level that would occur during deep-space missions of long
duration pose a risk to the integrity and function of the central nervous system?
16. Radiation protection of ionizing radiation from radiation sources is particularly difficult. Give a
reason for this difficulty.
13.5.3 Essay questions
17. I always lock my radioactive material-use rooms. However, renovators came in during the
weekend, worked, and left the door open while they were on their lunch break. Am I responsible and
how can I prevent this from happening? Debate on the situation above to support your answer.
18. How can I ensure that personnel who work in my lab, but do not use radioactive material, do not
violate the security requirements? Debate to support your idea.
19. A Housekeeping staff member opens my radioactive material-use room after working hours and
does not lock it when they leave. What should I do? Explain clearly to support your idea.
20. Make a research and predict what steps that can or might be taken to reduce the exposure to
radiation (consider if living near a radioactive area like an abandoned uranium mine, if finding a
radioactive source, or in the event of a nuclear explosion or accident).
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UNIT 14: COSMOLOGY, GALAXIES AND EXPANSION OF
UNIVERSE
Key unit Competence
By the end of the unit the learner should be able to explain the origin, the structure and the evolution
of the Universe.
My goals
Outline types of galaxies and cluster of galaxies.
Explain the structure of Milky way galaxy and earth’s position
Apply planetary motion knowledge to explain phenomena of planet motion.
Explain Doppler shift due to cosmic expansion.
State Hubble’s law.
Explain the big bang theory and relate to the expansion of universe.
Introductory activity
1. (a) Why are there different types of stars, such as red giants and white dwarfs, as well as main-
sequence stars?
(b) Were they all born this way, in the beginning? Or might each different type represent a
different age in the life cycle of a star?
2. How can astronomers tell the galaxies are moving away? How the explosion at the beginning can
explain such expansion?
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14.1 GALAXIES AND CLUSTERS
Activity 14.1 Our place in the Universe
1. Our planet is the Earth and it orbits around the Sun, does the sun orbit anything?
2. How does the sun interact with other objects in the Universe?
14.1.1 The structure of the Milky Way Galaxy
The Milky Way is our own galaxy. It is a spiral galaxy, composed of three parts:
The disk. Most of the stars in the Milky Way are located in a disk about 2 kpc thick, and about
40 kpc across. A parsec (pc) is a unit of distance commonly used in astronomy, 1pc=3.86x1016
m=3.26 ly. The disk is composed primarily of hot, young stars, and contains lots of dust and gas.
The bulge. The bulge lies in the center of the galaxy. It is about 6 kpc across, and extends above
and below the disk. There is very little gas or dust which are the material required to form new
stars. Therefore the bulge consists mainly of old stars.
The halo. The halo is primarily made up of globular clusters, and is roughly spherical in shape. It
is centered on the center of the galaxy, and is about 30 kpc to 40 kpc in radius. Again, there is
very little dust and gas. The halo is primarily composed of old stars. Interestingly, most of these
stars are low metallicity stars, which mean that they have even fewer metals than the Sun.
Our Galaxy has a diameter of almost 100 000 light-years and a thickness of roughly 2000 ly. It has a
central bulge and spiral arms (Fig.14.1).
Fig.14. 1 Milky Way Galaxy: (a) “edge view” in the plane of the disk; (b) “top view” looking down on the disk. (c)
Infrared photograph of the Milky Way galactic plane, showing the central bulge and disk of our Galaxy
(Douglass, PHYSICS, Principles with applications., 2014).
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Our Sun, which is a star like many others, is located about halfway from the galactic centre to the
edge, some 26 000 ly (8.5 kpc) from the centre. Our Galaxy contains roughly 400 billion stars (910400 ). The Sun orbits the galactic centre approximately once every 220 million years, so its
speed is roughly skm/200 relative to the centre of the Galaxy. There is also strong evidence that our
Galaxy is permeated and surrounded by a massive invisible “halo” of “dark matter”
In 1915, Shapley attempted to figure out the location of the center of the galaxy by mapping out the
positions of globular clusters. A globular cluster is a group of hundreds of thousands of stars, all
tightly bound together in a ball 20 pc to100 pc across. They have a very distinctive appearance, and
so are easy to find (Halliday, Resneck, & Walker, 2007).
He discovered that 20% of the clusters lay in the direction of the constellation Sagittarius, and
occupied only about 2% of the sky, and inferred that the bulk of the Galaxy must lie in that direction.
He used RR Lyrae stars to estimate the distances to the globular clusters. He found that these
globular clusters are centered on a point about 15 kpc from the Sun. Shapley reasoned that if the
clusters were distributed evenly about the Galaxy (and there’s no reason to think they shouldn’t be),
then the center of the Galaxy lies in the direction of Sagittarius, about 15 kpc away. Shapley didn’t
know about dust and consequently he overestimated the distance to the center of the Galaxy by a
factor of two. The center is actually about 8.5 kpc away (Douglass, PHYSICS, Principles with
applications., 2014).
Example 14.1: Our Galaxy’s mass
1Estimate the total mass of our Galaxy using the orbital data above for the Sun about the centre of
the Galaxy. Assume the mass of the Galaxy is concentrated in the central bulge.
Answer
We assume that the Sun (including our solar system) has total mass m and moves in a circular orbit
about the centre of the Galaxy (total mass M), and that the mass M can be considered as being
located at the centre of the Galaxy. We then apply Newton’s second law, maF with a being the
centripetal acceleration, r
va
2
and for F we use the universal law of gravitation
Our Sun and solar system orbit the center of the Galaxy, according to the best measurements as
mentioned above, with a speed of about v at a distance r from the Galaxy center we use Newton’s
second law:
𝐺𝑀𝑚
𝑟2=
𝑚𝑣2
𝑟, 𝑀 =
(26000𝑙𝑦)(1016𝑚
𝑙𝑦)(2𝑥105𝑚/𝑠)2
6.67𝑥10−11𝑁. 𝑚2/𝑘𝑔2= 1.56𝑥1041𝑘𝑔
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14.1.2 Types of galaxies
There are three main types of galaxies: Elliptical, Spiral, and Irregular. Two of these three types are
further divided and classified into a system that is now known the tuning fork diagram Fig 14.2.
When Hubble first created this diagram, he believed that this was an evolutionary sequence as well
as a classification. He believed that all galaxies started out as E0 ellipticals and evolved into spirals,
as the galaxy flattened out and developed arms. Astronomers have found today that instead, possibly
it is the other way around. The spiral galaxies sometimes merge to form elliptical galaxies (Linda,
2004)
Fig.14. 2 The Hubble’s tuning fork, a model of classification of galaxies developed by Edwin Hubble.
a. Spirals
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Fig.14. 3 (a) Spiral galaxy NGC 1365 (b) Spiral galaxy M100
Spiral galaxies have three main components: a bulge, disk, and halo. The bulge is a spherical
structure found in the center of the galaxy. This feature mostly contains reddish, older stars. The disk
is made up of dust, gas, and bluish, younger stars. The disk forms arm structures. Our Sun is located
in one of the arms, called the Orion arm which is thought to be an offshoot of the Sagittarius arm in
our galaxy, the Milky Way.
The halo of a galaxy is a loose, spherical structure located around the bulge and some of the disk.
The halo contains reddish, old clusters of stars, known as globular clusters
Fig.14. 4 The structure of galaxy
Spiral galaxies are classified into two groups, ordinary and barred. The ordinary group is
designated by S, and the barred group by SB. In normal spirals (as seen Fig.14.5) the arms originate
directly from the nucleus, or bulge, where in the barred spirals (see Fig.14.5) there is a bar of
material that runs through the nucleus that the arms emerge from. Both of these types are given a
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classification according to how tightly their arms are wound. The classifications are a, b, c, d ... with
"a" having the tightest arms. In type "a", the arms are usually not well defined and form almost a
circular pattern. Sometimes you will see the classification of a galaxy with two lower case letters.
This means that the tightness of the spiral structure is halfway between those two letters.
Fig.14. 5 The different shapes of Ordinary Group of Spiral galaxies
A barred spiral is very much like a spiral, except that the bulge is elongated, forming a bar across
the centre. The barred spirals are also subdivided into three classes: SBa, SBb, and SBc. Once again,
these subclasses indicate the relative size of the bulge.
Fig.14. 6 The different shapes of Barred spiral galaxies
S0 galaxies are an intermediate type of galaxy between E7 and a "true" spiral Sa. They differ from
elliptical because they have a bulge and a thin disk, but are different from Sa because they have no
spiral structure. S0 galaxies are also known as lenticular galaxies.
b. Elliptical galaxies
Elliptical galaxies are shaped like a spheroid, or elongated sphere. They have no arms and no disk.
They are big blobs of reddish, older stars. In the sky, where we can only see two of their three
dimensions, these galaxies look like elliptical, or oval, shaped disks. The lighting is smooth, with the
surface brightness decreasing as you go farther out from the center.
Fig.14. 7 Typical picture of the elliptical galaxy M87
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Elliptical galaxies are classified according to the elongation from a perfect circle (also known as the
ellipticity). The larger the number, the more elliptical the galaxy is. So, for example a galaxy of
classification of E0 appears to be perfectly circular, while a classification of E7 is very flattened (the
most elliptical). The elliptical scale varies from 0 to 7. Elliptical galaxies have no particular axis of
rotation.
Ellipticals galaxies can also be sorted by size:
Giant ellipticals are a few trillion parsecs across. They contain trillions of stars.
Dwarf ellipticals, on the other hand, are only about a thousand parsecs across, and contain
millions of stars.
There are many dwarf elliptical galaxies than the giants, but the giants are so large that they actually
contain most of the mass that is found in elliptical galaxies. Ellipticals contain very little gas and
dust. Fig. 14.8 shows a few elliptical galaxies.
Fig.14. 8 Elliptical galaxies
c. Irregulars
Irregular galaxies are all the galaxies that don’t fit in the other two categories. In general, they are
thought to be the result of collisions between galaxies. They contain a lot of dust and gas, and
consequently are full of young stars. They have no regular or symmetrical structure and the fraction
of such galaxies is very small.
They are divided into two groups, Irr I and Irr II. Irr I type galaxies have HII regions, which are
regions of elemental hydrogen gas, and many Population I stars, which are young hot stars. Irr II
galaxies simply seem to have large amounts of dust that block most of the light from the stars. All
this dust makes almost impossible to see distinctly stars in this kind of galaxies
Fig.14. 9 (a) Large Magellanic Cloud (Irr i) and (b) Antenna galaxies (NGC4038 and NGC4039) (Irr II)
14.1.3 Clusters of galaxies
In addition to stars both within and outside the Milky Way, we can see by telescope many faint
cloudy patches in the sky which were all referred to once as “nebulae” (Latin for “clouds”). A few of
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these, such as those in the constellations Andromeda and Orion, can actually be distinguished with
unaided eye on a clear night. A group of stars within a galaxy which are close to each other and held
together by gravitational attraction is called stellar cluster. Some are star clusters (Fig. 14.10a),
groups of stars that are so numerous they appear to be a cloud. Others are glowing clouds of gas or
dust (Fig. 14.10b), and it is for these that we now mainly reserve the word nebula.
Fig.14. 10 (a) This globular star cluster is located in the constellation Hercules. (b) This gaseous nebula, found in
the constellation Carina, is about 9000 light-years from us.
Most fascinating are those that belong to a third category: they often have fairly regular elliptical
shapes. Immanuel Kant (about 1755) guessed they are faint because they are a great distance beyond
our Galaxy. At first it was not universally accepted that these objects were extragalactic—that is,
outside our Galaxy. But the very large telescopes constructed in the twentieth century revealed that
individual stars could be resolved within these extragalactic objects and that many contain spiral
arms. Edwin Hubble (1889–1953) did much of this observational work in the 1920s using the 2.5 m
telescope on Mt. Wilson near Los Angeles, California, and then the world’s largest. Hubble
demonstrated that these objects were indeed extragalactic because of their great distances.
The distance to our nearest large galaxy, Andromeda, is over 2 million light-years, a distance
20 times greater than the diameter of our Galaxy. It seemed logical that these nebulae must be
galaxies similar to ours. (Note that it is usual to capitalize the word “galaxy” only when it refers to
our own.) Today it is thought there are roughly galaxies in the observable universe—that is,
roughly as many galaxies as there are stars in a galaxy. (See Fig. 14.11.)
1110
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Fig.14. 11. This image, called the Hubble Ultra Deep Field, offers a core sample of the deep universe with diverse
galaxies of various ages, sizes, shapes and colors.
Many galaxies tend to be grouped in galaxy clusters held together by their mutual gravitational
attraction. Our own, called local group, contains at least 28 galaxies. Of these, three are spirals,
eleven are irregulars and fourteen are ellipticals. There may be anywhere from a few dozen to many
thousands of galaxies in each cluster. Furthermore, clusters themselves seem to be organized into
even larger aggregates: clusters of clusters of galaxies, or superclusters.
Some astronomical measurements indicate that there is "something else" among the stars and
interstellar materials. This is called dark matter, because it cannot be seen, but it apparently has
mass and does affect other matter and gravitational fields. Although the so-called dark matter appears
to account for around 90% of the mass of most galaxies, the nature of this material is not well
understood. At the center of some galaxies, there may be super massive black holes. Again, they
cannot be seen but they are indicated on how they affect the nearby stars.
14.1.4 Checking my progress
1. List the three major classifications of Galaxies. What do they all have in common?
2. What is the name of the Galaxy that you live in?
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14.2 COSMOLOGY
Activity 14.2: How stars are formed
1. What does it mean that distant galaxies are all moving away from us, and with ever greater speed
the farther they are from us? Explain how the Hubble constant may be used to estimate the age of
the universe
2. How do stars form? What factors determine the masses, luminosities, and distribution of stars in
our Galaxy?
Cosmology aims to explain the origin and evolution of the Universe, the underlying physical
processes, and thereby to obtain a deeper understanding of the laws of Physics assumed to hold
throughout the Universe. Cosmology is the study of the history of the Universe as a whole, both its
structure and evolution.
The study assumes that over large distances the Universe looks essentially the same from any
location (the Universe is homogeneous) and that the Universe looks essentially the same in all
directions (the Universe is isotropic). The two assumptions are known as the cosmologicalprinciple.
In addition, it is assumed that the same laws of Physics hold everywhere in the Universe.
To study the evolution of the Universe, astronomers rely on observations of distant objects. For
example, the Andromeda Galaxy (M31) is about 2 million light years away. This means that our
photographs of M31 show the galaxy as it was 2 million years ago. The Virgo cluster of galaxies is
about 50 million light years away, and the information presently received by our telescopes describe
the state of the cluster as it was 50 million years ago. Information received from galaxies that are
billions of light years away pertains to the state of these objects as they were billions of years ago,
when they were much younger, possibly just forming. Receiving information from distant objects is
equivalent to receiving information from the past. This information is vital in reconstructing the
evolutionary stages of the galaxies, and the Universe as a whole.
14.2.1 Doppler shift due to cosmic expansion
Activity14.3: Doppler Effect
1. How Doppler Effect is used in communication with satellites?
2. How is the Doppler Effect used in Astronomy?
Movement toward or away from a source of radiation does indeed change the way we perceive the
radiation. Motion along any particular line of sight is known as radial motion. It should be
distinguished from transverse motion, which is perpendicular to the line of sight. Radial motion but-
not transverse motion- brings about changes in the observed properties of radiation.
In visible light, red light has the longest wavelength, and violet light the shortest. The light of an
object moving away from an observer is shifted toward longer wavelengths (red color). The light
from an object moving at a high speed toward an observer is shifted toward the color violet.
This change in the observed wavelength of a wave be it an electromagnetic (light) wave or an
acoustical (sound) wave is known as the Doppler Effect, in honor of Christian Doppler, the
nineteenth century Austrian physicist who first explained it.
353
Astronomers most often use the Doppler Effect to measure the velocity of galaxies, which are
moving away from Earth the (red-shift effect, a shift to lower frequencies) or toward the Earth
(blue-shift, toward shorter wavelength).
Blue-shift
The equation for the observed frequency of a light wave when the source is traveling toward you
(blue-shift) is:
b
b
cf f
c v
(14.01)
The blue-shift equation for wavelength is: bb
c v
c
(14.02)
where
fb is the observed blue-shift frequency
vb is the velocity of the source moving toward you
c is the speed of light. c >> vb (c is much greater than vs)
λb is the observed blue-shift wavelength
λ is the emitted wavelength (Greek symbol lambda)
Red-shift
The equation for the observed frequency of a light wave when the source is traveling away from you
(red-shift) is:
r
r
cf f
c v
(14.03)
The red-shift equation for wavelength is: rr
c v
c
(14.04)
Where
fr is the observed red-shift frequency,
vr is the velocity of the source moving away from you,
λr is the observed red-shift wavelength,
λ is the emitted wavelength (Greek symbol lambda)
Note that "−" and "+" are reversed as compared to the standard Doppler Effect equations of sound
waves.
354
In general, when an object is approaching or moving away, the wavelength of the light it emits (or
reflects) is changed. The shift of the wavelength, r , is directly related to the velocity, v, of
the object:
r r
c
v
(14.05)
This value is known as the cosmological redshift of a star, denoted
z .
- If z is positive, the star is moving away from us (receding object)- the wavelength is shifted up
towards the red end of the electromagnetic spectrum.
- If z is negative, the star is moving towards us. This is known as blue shift and the emitted
wavelength appears shorter
Example 14.2
1. If a distant galaxy is moving away from us at approximately 50 000 km/s and we approximate
the speed of light (λ = 434 nm, which is in the violet region of the visible spectrum) as
c = 300 000 km/s, calculate the resulting wavelength
Answer
the resulting wavelength will be: rr
c v
c
Substitute values into equation: 8 7
8
3 10 5 10434 520.8
3 10r nm nm
The line has shifted from violet to green.
Quick check 14.1: (a) M31 (the Andromeda galaxy) is approaching us at about 120 km s-1. What is
its red/blue-shift?
(b) Some light from M31 reaches us with a wavelength of 590 nm. What is its wavelength, relative
to M31?
Velocity
Typically, an astronomer would study the spectrum of a distant star or galaxy and measure the new
observed spectral lines of the various elements on the object.
Then the direction and velocity of the star or galaxy would be determined.
The blue-shift equation for velocity is: bbv C
(14.06)
355
The red-shift equation for velocity is: rrv C
(14.07)
Where is the wavelength emitted if the object is at rest and v is the component of the velocity
along the ‘‘line of sight’’ or the ‘‘radial velocity.’’
Example 14.3
1 Suppose that molecules at rest emit with a wavelength of 18 cm. You observe them at a
wavelength of 18.001 cm. How fast is the object moving and in which direction, towards or away
from you?
Answer
To find out how quickly, use the Doppler equation:
This problem calls for the Doppler equation. 0
0
cv
c
v
𝑣 =∆𝜆𝑐
𝜆𝑜=
(18.001 − 18)(3𝑥108)
18= 16.7𝑘𝑚/𝑠
The molecules are travelling with a radial speed of 16.7 km/s. Since the wavelength is longer, the
light has been red-shifted, or stretched out, and so the object is moving away from you.
Quick check 14.2. A radio spectrum of an interstellar cloud shows the 21 cm line shifted to 21.007
cm. Is the cloud approaching, receding, or remaining at the same distance from us? If it is travelling,
what is its speed?
14.2.2 The Hubble’s law
Activity 14.4: Hubble’s law
Discuss the limitations of Hubble’s law. Explain how the Hubble constant may be determined.
Analysis of redshifts from many distant galaxies led Edwin Hubble to a remarkable conclusion. The
speed of recession of a galaxy is proportional to its distance from us (Fig. 14.10). This relationship is
now called the Hubble law; expressed as an equation,
(14.11)
where
- 0 71 / /H km s Mpc is called the Hubble constant, since at any given time it is constant over
space.
rHv 0
356
- r the distance of the galaxy from the Earth
Determining has been a key goal of the Hubble Space Telescope, which can measure distances to
galaxies with unprecedented accuracy. It is determined by calculating the slope in the plot velocity of
galaxies versus distance (see fig below).
The current best value is 118
0 103.2 sH with an uncertainty of 5%.
Fig.14. 12 Graph of recession speed versus distance for several galaxies. The best-fit straight line illustrates
Hubble’s law. The slope of the line is the Hubble constant
The is then commonly expressed in the mixed units (kilometers per second per megaparsec), where
= 3.08610 x 1019 km
(14.12)
18 1 19
0 2.3 10 (3.086 10 / ) 71km/ s/ MpcH s km Mpc
Example 14.4
1. The spectral lines of various elements are detected in light from a galaxy in the constellation
Ursa Major. An ultraviolet line from singly ionized calcium 393nm is observed at wavelength
414r nm red-shifted into the visible portion of the spectrum.
(a) At what speed is this galaxy receding from us?
(b) Use the Hubble law to find the distance from earth to the galaxy
Answer
0H
pcMpc 6101
Mpc
skm
Mpc
ly
pc
kmsH
/71)
1
26.3)(
1
1046.9)(103.2(
12118
0
357
(a) This example uses the relationship between redshift and recession speed for a distant galaxy.
We can use the wavelengths at which the light is emitted and r that we detect on earth in Eq.
(14.05) to determine the galaxy’s recession speed v if the fractional wavelength shift is not too
great.
The redshift is z =lr- l
l= 0.053
For high redshift the speed is obtained by the following formula:
𝑣 = 𝑧𝑐 = 0.053𝑐 = 1.59𝑥107𝑚/𝑠
(b) Use the Hubble law to find the distance from Earth to the galaxy
Answer
The Hubble law relates the redshift of a distant galaxy to its distance r from earth. We solve Eq.
for r and substitute the recession speed v from Eq
To appreciate the immensity of this distance, consider that our farthest-ranging unmanned
spacecraft have traveled only about 0.001 ly from our planet.
Another aspect of Hubble’s observations was that, in all directions, distant galaxies appeared to be
receding from us. There is no particular reason to think that our Galaxy is at the very center of the
Universe; if we lived in some other galaxy, every distant galaxy would still seem to be moving away.
That is, at any given time, the universe looks more or less the same, no matter where in the universe
we are. This important idea is called the cosmological principle. There are local fluctuations in
density, but on average, the universe looks the same from all locations. Thus the Hubble constant is
constant in space although not necessarily constant in time, and the laws of Physics are the same
everywhere.
14.2.4 The Big Bang theory and expansion of Universe
Activity 14.5: Stellar expansion
1. How does the curvature of the universe affect its future destiny?
2. Describe some of the evidence that the universe started with a “Big Bang.”
3. How does dark energy affect the possible future of the universe?
4. Explain how the big bang theory explains the observed Doppler Shifts of Galaxies.
The major theory of how the Universe started is the "Big Bang" theory. This states that about 13.7
billion years ago (13 700 000 000 years) all matter was compressed to what some estimate was the
size of a golf ball. It then expanded in a "big bang" and spread out until it has reached the enormous
size of the present-day Universe. While the matter was spreading out, it started to clump together
rHv 0
mlyMpc
Mpc
skm
sm
H
vr 248
4
7
0
107.6101.7220/
101.7
/1055.1
358
into larger and larger masses. The turbulence of the expansion resulted in the spinning of the
galaxies.
The whole idea of the Big Bang theory came when astronomers noticed that distant nebulas (or more
correctly, nebulae) and galaxies were all moving away from us. It was also seen that they were
moving away at speeds proportional to their distance from us. Since it is assumed that our galaxy is
also moving in some direction, it was calculated that all of the galaxies in the universe were moving
away from some given point in space.
The way astronomers were able to estimate the speed of the galaxies is by what is called the "red-
shift" of their light. The red-shift is a form of Doppler Effect with light, such that when an object is
moving away from you at high speeds, the light shifts towards lower frequencies.
Measurements show that the Universe is still expanding. By interpolating the directions and
velocities backward, astronomers have estimated the beginning time of the explosion. Of course,
such measurements are highly inaccurate. There is debate on this theory and whether the Universe
will continue to expand or will start to contract.
The Hubble law suggests that at some time in the past, all the matter in the universe was far more
concentrated than it is today. It was then blown apart in an immense explosion called the Big Bang,
giving all observable matter more or less the velocities that we observe today.
When did this happen? According to the Hubble law, matter at a distance away from us is traveling
with speed v. The time needed to travel a distance is
By this hypothesis the Big Bang occurred about 14 billion years ago. It assumes that all speeds are
constant after the Big Bang; that is, it neglects any change in the expansion rate due to gravitational
attraction or other effects. We’ll return to this point later. For now, however, notice that the age of
the earth determined from radioactive dating is 4.54 billion years. It’s encouraging that our
hypothesis tells us that the universe is older than the earth!
The expansion of the universe suggests that typical objects in the universe were once much closer
together than they are now. This is the basis for the idea that the universe began about 14 billion
years ago as an expansion from a state of very high density and temperature known affectionately as
the Big Bang.
The birth of the universe was not an explosion, because an explosion blows pieces out into the
surrounding space. Instead, the Big Bang was the start of an expansion of space itself. However,
after the expansion of the universe, matter exploded into stars and galaxies. The observable universe
was relatively very small at the start and has been expanding, getting ever larger, ever since. The
initial tiny universe of extremely dense matter is not to be thought of as a concentrated mass in the
midst of a much larger space around it. The initial tiny but dense universe was the entire universe.
There wouldn’t have been anything else. When we say that the universe was once smaller than it is
now, we mean that the average separation between objects (such as electrons or galaxies) was less.
The universe may have been infinite in extent even then, and it may still be now (only bigger). The
observable universe (that which we have the possibility of observing because light has had time to
reach us) is, however, finite.
ysHrH
r
v
rt 1017
00
104.1103.41
359
360
14.2.4 Stellar evolution
Activity14.6: How are stars born
1. Explain why giants are not in the main sequence on the H-R diagram.
2. How do their temperatures and absolute magnitudes compare with those of main sequence stars?
It is believed that stars are born, when gaseous clouds (mostly hydrogen) and dust called a nebula
contract due to the pull of gravity. Gravitational forces cause instability within the nebula. A huge
gas cloud might fragment into numerous contracting masses, each mass centered in an area where the
density is only slightly greater than that at nearby points. Once such “globules” form, gravity causes
each to contract in toward its center of mass see Fig.14.13.
As the particles of such a protostar accelerate inward, their kinetic energy increases. Eventually,
when the kinetic energy is sufficiently high, the Coulomb repulsion between the positive charges is
not strong enough to keep all the hydrogen nuclei apart, and nuclear fusion can take place. When the
particles in the smaller clouds move closer together, the temperatures in each nebula increase. As
temperatures inside each nebula reach 10 000 000 K, fusion begins. The energy released radiates
outward through the condensing ball of gas. As the energy radiates into space, stars are born.
Fig.14. 13 Lifecycle of stars
In a star like our Sun, the fusion of hydrogen (sometimes referred to as “burning”) occurs via the
proton–proton chain, in which four protons fuse to form a He4
2 nucleus with the release of rays,
positrons, and neutrinos:
1 4
1 24 2 2 2eH He e
These reactions require a temperature of about K710 , corresponding to an average kinetic energy of
about 1 keV.
The tremendous release of energy in this fusion reaction produces an outward pressure sufficient to
halt the inward gravitational contraction.
361
Our protostar, now really a young star, stabilizes on the main sequence. Exactly where the star falls
along the main sequence depends on its mass. The more massive the star, the farther up (and to the
left) it falls on the H–R diagram of Fig. 14.14.
Fig.14. 14 Hertzsprung–Russell (H–R) diagram is a logarithmic graph of luminosity vs. surface temperature T of
stars (note that T increases to the left).
Our Sun required perhaps 30 million years to reach the main sequence, and is expected to remain
there about 10 billion years ( yr1010 ) but a star ten times more massive may reside there for only
yr710
More massive stars have shorter lives, because they are hotter and the Coulomb repulsion is more
easily overcome, so they use up their fuel faster. As it moves upward, it enters the red giant stage.
Thus, theory explains the origin of red giants as a natural step in a star’s evolution.
As hydrogen fuses to form helium, the helium that is formed is denser and tends to accumulate in the
central core where it was formed. As the core of helium grows, hydrogen continues to fuse in a shell
around it.
When much of the hydrogen within the core has been consumed, the production of energy decreases
at the center and is no longer sufficient to prevent the huge gravitational forces from once again
causing the core to contract and heat up.
The hydrogen in the shell around the core then fuses even more aggressively because of this rise in
temperature, allowing the outer envelope of the star to expand and to cool. The surface temperature,
thus reduced, produces a spectrum of light that peaks at longer wavelength (reddish). This process
marks a new step in the evolution of a star. The star has become redder, it has grown in size, and it
362
has become more luminous, which means it has left the main sequence. It will have moved to the
right and upward on the on the H–R diagram, as it moves upward, it enters the red giant stageas
shown in Fig. 14.15
Fig.14. 15 Evolutionary “track” of a star like our Sun represented on an H–R diagram.
Our Sun, for example, has been on the main sequence for about 4.5 billion years. It will probably
remain there another 5 billion years or 6 billion years. When our Sun leaves the main sequence, it is
expected to grow in diameter (as it becomes a red giant) by a factor of 100 or more, possibly
swallowing up inner planets such as Mercury and possibly Venus and even Earth.
If the star is like our Sun, or larger, further fusion can occur. As the star’s outer envelope expands, its
core continues to shrink and heat up.
When the temperature reaches about even helium nuclei, in spite of their greater charge and
hence greater electrical repulsion, can come close enough to each other to undergo fusion. The
reactions are
with the emission of two rays.
These two reactions must occur in quick succession (because is very unstable), and the net effect
is
This fusion of helium causes a change in the star which moves rapidly to the “horizontal branch” on
the H–R diagram (Fig. 14.15). Further fusion reactions are possible, with fusing with to
form
K810
BeHeHe 8
4
4
2
4
2
CBeHe 12
6
8
4
4
2
Be8
4
23 12
6
8
4
4
2 CBeHe
He4
2C12
6
O16
8
363
In more massive stars, higher Z elements like or can be made. This process of creating
heavier nuclei from lighter ones (or by absorption of neutrons which tends to occur at higher Z) is
called nucleosynthesis.
Low Mass Stars—White Dwarfs
After the star’s core uses up its supply of helium, it contracts even more. As the core of a star like the
sun runs out of fuel, the outer layers escape into space. This leaves behind the hot, dense core. The
core contracts under the force of gravity. At this stage in a star’s evolution, it is a white dwarf. A
white dwarf is about the size of Earth.
Stars born with a mass less than about 8 solar masses eventually end up with a residual mass less
than about 1.4 solar masses. A residual mass of 1.4 solar masses is known as the Chandrasekhar
limit.
For stars smaller than this, no further fusion energy can be obtained because of the large Coulomb
repulsion between nuclei. The core of such a “low mass” star (original solar masses) contracts under
gravity. The outer envelope expands again and the star becomes an even brighter and larger red
giant, Fig.14.15. Eventually the outer layers escape into space, and the newly revealed surface is
hotter than before. So the star moves to the left in the H–R diagram see Fig.14.15. Then, as the core
shrinks the star cools, and typically follows the downward, becoming a white dwarf. A white dwarf
with a residual mass equal to that of the Sun would be about the size of the Earth.
A white dwarf contracts to the point at which the electrons start to overlap, but no further because, by
the Pauli exclusion principle, no two electrons can be in the same quantum state. At this point the
star is supported against further collapse by this electron degeneracy pressure. A white dwarf
continues to lose internal energy by radiation, decreasing in temperature and becoming dimmer until
it glows no more. It has then become a cold dark chunk of extremely dense material.
Supergiant and supernova
In stars that are over ten times more massive than our sun, the stages of evolution occur more quickly
and more violently. The core heats up to much higher temperatures. Heavier elements form by
fusion. The star expands into a supergiant. Eventually, iron forms in the core. Fusion can no longer
occur once iron is obtained. In fact, iron is so tightly bound that no energy can be extracted by
fusion. However, when it happen that Iron fuses, it absorbs energy in the process and the cote
temperature and pressure drop. The core collapses violently, sending a shock wave outward through
the star. The outer portion of the star explode, producing a supernova. A supernova can be millions
of times brighter than the original star.
Neutron stars and black holes
The collapsed core of a supernova shrinks to about 10 km to 15 km. only neutrons can exist in dense
core, and the supernova becomes a neutron star. If the remaining dense core is over three times more
massive than the sun, probably nothing can stop the core’s collapse. It quickly evolves into a
blackhole- an object so dense, nothing can escape its gravity field. In fact, not even light can escape
a black hole.
Nebulas
Ne20
10 Mg24
12
364
A star begins its life as a nebula, but where does the matter in nebula come from? Nebulas form
partly from the matter that was once in other stars. This matter can be incorporated into other
nebulas, which can evolve into new stars. The matter in stars is recycled many times. However, when
it happen that iron fuse, it absorbs energy in the process and the core temperature and pressure drops.
14.2.5 Checking my progress
1. If the velocity of the source was 0.1c toward you, what would be the new frequency?
A. 1.1 c
B. 1.1 f
C. Not enough information
2. If c = 186 000 mi/s and vr = 6 000 mi/s away from the Earth, what would be the observed
wavelength?
A. 1.03 λ
B. 0.97 λ
C.
3. If the observed wavelength λr equals the emitted wavelength, what is vr?
A. c
B.
C. 0
4. About how far does light travel in 1/10 second?
A. 18 600 miles or 30 000 km
B. 186 000 miles or 300 000 km
C. 1 860 000 miles or 3 000 000 km
5. Why does light bend when it goes through glass at an angle?
A. It goes faster, causing the beam to bend
B. It goes slower, causing the beam to bend
C. Light can't pass through glass
6. What happens when matter travels at 190 000 miles/sec or 310 000 km/s?
A. The matter heats up because of the high speed
B. It becomes invisible to most people
C. Matter can't go faster than the speed of light
7. Where is the speed of light highest? Speed of light is maximum in water, air or steel?
9. Some light has a wavelength, relative to M31, of 480 nm. What is its wavelength, relative to us?
2
c
365
366
14.3 END UNIT ASSESSMENT
14.3.1 Multiple choices:
1. What is a result of the Big Bang Theory?
A. Not Sure
B. An estimate of how many years ago the Universe began
C. An explanation of life on Earth
D. The disproving of the Theory of Relativity
2. How did ancient people discover things about astronomy?
A. Not Sure C. They read it in a book
B. They were observant D. They worshiped the Sun god
3. Why do they call it dark matter?
A. Not Sure C. Because it is a dark brown color
B. Because it is very heavy D. Because no one has seen it
4. What planet is known for its rings?
A. Not Sure C. Earth
B. Mars D. Saturn
14.3.2 Solve these problems
5. The Sun (and everything else in the Galaxy), is in orbit around the center. The Sun’s velocity is
220 km/s. The Sun’s galactic radius is 8.5 kpc. Using the velocity of the Sun (220 km/s), and its
distance from the center of the Milky Way (8 500 pc), calculate how long it takes the Sun to orbit the
center.
6. Describe how we can estimate the distance from us to other stars. Which methods can we use for
nearby stars, and which can we use for very distant stars? Which method gives the most accurate
distance measurements for the most distant stars?
7. GEAT THINKERS KRISS KROSS: Fill the names of these famous scientists and thinkers into
the puzzle. We’ve filled in one name to get you started.
4 letters: CROSS (English physician)
5 letters:
GAMON (Russian-born American physicist)
GAUSS (German mathemathician and astronomer)
MORSE (American inventer)
6 letters:
DARWIN (English naturalist)
EDSON ( American inventor)
EUCLID (Greeek mathematician and physicist)
367
JENNER (English physicist)
7 letters:
FARADAY (English physicist and chemist)
Pasteur (French chemist)
PAULING (American chemist)
PTOLEMY (Greek-Egyptian astronomer and geographer)
10 letters: Aristarchus (Greek astronomer)
7.
C O P E R N I C U S
8. Find and circle the hidden science words. Look up, down, across, diagonally, and backward.
Air, atmosphere, bacteria, bolt, chemical, gas, mineral, odor, ozone, temperature, thunder, vapor,
virus, water.
E S A G X D I Q A A A
G R P A T L Y J I T I
T H U N D E R R W M R
Z R E T A W I S F O E
L B D E A K U B D S T
R O F J R R Z O O P C
O L A C I M E H C H A
P T N V H X G P R E B
A I O Z O N E L M R S
V T P F V T S V X E O
M I N E R A L Q I Y T
9. Fit the names of these famous scientists and thinkers into the puzzle. We have filled in one name
to get you started.
3 letters: LEE (Chinese-born American physicist)
368
4 letters:
BELL (Scottish-born American inventor)
BOHR (Danish physicist)
YOUNG (Chinese-born American physicist)
5 letters
CURIE (Polish-born French chemist and physicist)
SOGAN (American astronomer)
6 letters:
FERMAT (French mathematician)
MENDEL (Austrian botanist)
NEWTON (English mathematician and scientist)
7 letters
EHRLICH (German bacteriologist)
GALILEO (Italian astronomer and physicist)
LEIBNIZ (German philosopher and mathematician)
MARCONI (Italian engineer and inventor)
MAXWELL (Scottish physicist)
8 letters
EINSTEIN (German-born American theoretical physicist)
FRANKLIN (American statesman and scientist)
LINNAEUS (Swedish botanist)
E
I
N
S
T
E
I
N
10. INTERPLANETARY WORD FIND: Find and circle the hidden words. Look up, down, across,
diagonally, and backward
Earth, Galaxy, Jupiter, Mars, Meteor, Moon, Orbit, Planet, Pluto, Ring, Satellite, Saturn, Sun,
Telesphore, Venus
369
A N Y Y H T R A E A M
R I N G N R U T A S X
W S O M Z P I V O U R
H K R V G L M O O N T
M I B T L A Q G B P R
J E I E S N L U N S E
M G T U O E D A K J T
F A N E L T F H X E I
S E R P O W U T R Y P
V Q W S A R I L D E U
L T E L E S C O P E J
370
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